This document provides an overview of optimization techniques. It begins with an introduction to optimization and examples of optimization problems. It then discusses the historical development of optimization methods. The document categorizes optimization problems into convex, concave, and subclasses like linear programming, quadratic programming, and semidefinite programming. It also covers advanced optimization methods like interior point methods. Finally, the document discusses applications of convex optimization techniques in fields such as engineering, finance, and wireless communications.
This document provides an overview of dynamic programming. It begins by explaining that dynamic programming is a technique for solving optimization problems by breaking them down into overlapping subproblems and storing the results of solved subproblems in a table to avoid recomputing them. It then provides examples of problems that can be solved using dynamic programming, including Fibonacci numbers, binomial coefficients, shortest paths, and optimal binary search trees. The key aspects of dynamic programming algorithms, including defining subproblems and combining their solutions, are also outlined.
Penalty Function Method For Solving Fuzzy Nonlinear Programming Problempaperpublications3
Abstract: In this work, the fuzzy nonlinear programming problem (FNLPP) has been developed and their result have also discussed. The numerical solutions of crisp problems and have been compared and the fuzzy solution and its effectiveness have also been presented and discussed. The penalty function method has been developed and mixed with Nelder and Mend’s algorithm of direct optimization problem solutionhave been used together to solve this FNLPP.
Keyword:Fuzzy set theory, fuzzy numbers, decision making, nonlinear programming, Nelder and Mend’s algorithm, penalty function method.
This document provides an overview of machine learning topics, including supervised learning techniques like linear regression, logistic regression, support vector machines, and decision trees. Unsupervised learning methods like clustering and dimensionality reduction are also summarized. Deep learning approaches such as neural networks, convolutional neural networks, and recurrent neural networks are introduced. The document concludes with sections on machine learning tips/tricks and probability/statistics refreshers.
Penalty Function Method For Solving Fuzzy Nonlinear Programming Problempaperpublications3
Abstract: In this work, the fuzzy nonlinear programming problem (FNLPP) has been developed and their result have also discussed. The numerical solutions of crisp problems and have been compared and the fuzzy solution and its effectiveness have also been presented and discussed. The penalty function method has been developed and mixed with Nelder and Mend’s algorithm of direct optimization problem solutionhave been used together to solve this FNLPP.Keyword:Fuzzy set theory, fuzzy numbers, decision making, nonlinear programming, Nelder and Mend’s algorithm, penalty function method.
Title:Penalty Function Method For Solving Fuzzy Nonlinear Programming Problem
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This document discusses dynamic programming and provides examples to illustrate the technique. It begins by defining dynamic programming as a bottom-up approach to problem solving where solutions to smaller subproblems are stored and built upon to solve larger problems. It then provides examples of dynamic programming algorithms for calculating Fibonacci numbers, binomial coefficients, and finding shortest paths using Floyd's algorithm. The key aspects of dynamic programming like avoiding recomputing solutions and storing intermediate results in tables are emphasized.
The document discusses dynamic programming and its application to the matrix chain multiplication problem. It begins by explaining dynamic programming as a bottom-up approach to solving problems by storing solutions to subproblems. It then details the matrix chain multiplication problem of finding the optimal way to parenthesize the multiplication of a chain of matrices to minimize operations. Finally, it provides an example applying dynamic programming to the matrix chain multiplication problem, showing the construction of cost and split tables to recursively build the optimal solution.
Dynamic programming is a technique that breaks problems into subproblems and saves results to optimize solutions without recomputing subproblems. It is commonly used in computer science, mathematics, economics, and operations research for problems like the Fibonacci series, knapsack problem, and traveling salesman problem. Dynamic programming improves efficiency by storing subproblem solutions and avoiding redundant calculations. It can find optimal and approximate solutions to large problems. For the Fibonacci series, a dynamic programming approach builds up the sequence by calculating each term from the previous two terms rather than recursively calculating all subproblems.
This document provides an overview of optimization techniques. It begins with an introduction to optimization and examples of optimization problems. It then discusses the historical development of optimization methods. The document categorizes optimization problems into convex, concave, and subclasses like linear programming, quadratic programming, and semidefinite programming. It also covers advanced optimization methods like interior point methods. Finally, the document discusses applications of convex optimization techniques in fields such as engineering, finance, and wireless communications.
This document provides an overview of dynamic programming. It begins by explaining that dynamic programming is a technique for solving optimization problems by breaking them down into overlapping subproblems and storing the results of solved subproblems in a table to avoid recomputing them. It then provides examples of problems that can be solved using dynamic programming, including Fibonacci numbers, binomial coefficients, shortest paths, and optimal binary search trees. The key aspects of dynamic programming algorithms, including defining subproblems and combining their solutions, are also outlined.
Penalty Function Method For Solving Fuzzy Nonlinear Programming Problempaperpublications3
Abstract: In this work, the fuzzy nonlinear programming problem (FNLPP) has been developed and their result have also discussed. The numerical solutions of crisp problems and have been compared and the fuzzy solution and its effectiveness have also been presented and discussed. The penalty function method has been developed and mixed with Nelder and Mend’s algorithm of direct optimization problem solutionhave been used together to solve this FNLPP.
Keyword:Fuzzy set theory, fuzzy numbers, decision making, nonlinear programming, Nelder and Mend’s algorithm, penalty function method.
This document provides an overview of machine learning topics, including supervised learning techniques like linear regression, logistic regression, support vector machines, and decision trees. Unsupervised learning methods like clustering and dimensionality reduction are also summarized. Deep learning approaches such as neural networks, convolutional neural networks, and recurrent neural networks are introduced. The document concludes with sections on machine learning tips/tricks and probability/statistics refreshers.
Penalty Function Method For Solving Fuzzy Nonlinear Programming Problempaperpublications3
Abstract: In this work, the fuzzy nonlinear programming problem (FNLPP) has been developed and their result have also discussed. The numerical solutions of crisp problems and have been compared and the fuzzy solution and its effectiveness have also been presented and discussed. The penalty function method has been developed and mixed with Nelder and Mend’s algorithm of direct optimization problem solutionhave been used together to solve this FNLPP.Keyword:Fuzzy set theory, fuzzy numbers, decision making, nonlinear programming, Nelder and Mend’s algorithm, penalty function method.
Title:Penalty Function Method For Solving Fuzzy Nonlinear Programming Problem
Author:A.F.Jameel, Radhi.A.Z
International Journal of Recent Research in Mathematics Computer Science and Information Technology (IJRRMCSIT)
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This document discusses dynamic programming and provides examples to illustrate the technique. It begins by defining dynamic programming as a bottom-up approach to problem solving where solutions to smaller subproblems are stored and built upon to solve larger problems. It then provides examples of dynamic programming algorithms for calculating Fibonacci numbers, binomial coefficients, and finding shortest paths using Floyd's algorithm. The key aspects of dynamic programming like avoiding recomputing solutions and storing intermediate results in tables are emphasized.
The document discusses dynamic programming and its application to the matrix chain multiplication problem. It begins by explaining dynamic programming as a bottom-up approach to solving problems by storing solutions to subproblems. It then details the matrix chain multiplication problem of finding the optimal way to parenthesize the multiplication of a chain of matrices to minimize operations. Finally, it provides an example applying dynamic programming to the matrix chain multiplication problem, showing the construction of cost and split tables to recursively build the optimal solution.
Dynamic programming is a technique that breaks problems into subproblems and saves results to optimize solutions without recomputing subproblems. It is commonly used in computer science, mathematics, economics, and operations research for problems like the Fibonacci series, knapsack problem, and traveling salesman problem. Dynamic programming improves efficiency by storing subproblem solutions and avoiding redundant calculations. It can find optimal and approximate solutions to large problems. For the Fibonacci series, a dynamic programming approach builds up the sequence by calculating each term from the previous two terms rather than recursively calculating all subproblems.
This document discusses nonlinear programming (NLP) problems. NLP problems involve objective functions and/or constraints that contain nonlinear terms, making them more difficult to solve than linear programs. While exact solutions cannot always be found, algorithms can typically find approximate solutions within an acceptable error range of the optimum. However, for some NLP problems there is no reliable way to find the global maximum, as algorithms may stop at a local maximum instead. The document describes different types of NLP problems and techniques for solving them, including using Excel Solver with multiple starting values to attempt finding the global rather than just local optima.
1. An algorithm is a sequence of unambiguous instructions to solve a problem within a finite amount of time. It takes an input, processes it, and produces an output.
2. Designing an algorithm involves understanding the problem, choosing a computational model and problem-solving approach, designing and proving the algorithm's correctness, analyzing its efficiency, coding it, and testing it.
3. Important algorithm design techniques include brute force, divide and conquer, decrease and conquer, transform and conquer, dynamic programming, and greedy algorithms.
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For some management programming problems, multiple objectives to be optimized rather than a single objective, and objectives can be expressed with ratio equations such as return/investment, operating
profit/net-sales, profit/manufacturing cost, etc. In this paper, we proposed the transformation characteristics to solve the multi objective linear fractional programming (MOLFP) problems. If a MOLFP problem with both the numerators and the denominators of the objectives are linear functions and some
technical linear restrictions are satisfied, then it is defined as a multi objective linear fractional programming problem MOLFPP in this research. The transformation characteristics are illustrated and the solution procedure and numerical example are presented.
For some management programming problems, multiple objectives to be optimized rather than a single objective, and objectives can be expressed with ratio equations such as return/investment, operating profit/net-sales, profit/manufacturing cost, etc. In this paper, we proposed the transformation characteristics to solve the multi objective linear fractional programming (MOLFP) problems. If a MOLFP problem with both the numerators and the denominators of the objectives are linear functions and some technical linear restrictions are satisfied, then it is defined as a multi objective linear fractional programming problem MOLFPP in this research. The transformation characteristics are illustrated and the solution procedure and numerical example are presented.
This document provides an overview of optimization capabilities in the free and open source software Scilab. It discusses the Nelder-Mead optimization component recently added to Scilab, which performs nonlinear optimization without requiring gradients. The document also compares Scilab's optimization solvers to those in MATLAB, finding that Scilab has similar functionality for problems like minimization, equation solving and least squares, though some solvers are only in alpha or beta versions. Finally, it outlines the OMD2 project which aims to develop Scilab into a full optimization platform through additional modules for data management, modeling and visualization.
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This document provides an overview of optimisation techniques for static and dynamic contexts. It discusses the principles of optimisation, including formulating problems with objective functions and constraints. It also covers topics like gradient vectors, Hessian matrices, unimodal/multimodal functions, and numerical methods for solving static optimisation problems. The document aims to provide an understanding of optimisation principles that can be applied to linear and nonlinear, unconstrained and constrained problems.
For some management programming problems, multiple objectives to be optimized rather than a single
objective, and objectives can be expressed with ratio equations such as return/investment, operating
profit/net-sales, profit/manufacturing cost, etc. In this paper, we proposed the transformation
characteristics to solve the multi objective linear fractional programming (MOLFP) problems. If a MOLFP
problem with both the numerators and the denominators of the objectives are linear functions and some
technical linear restrictions are satisfied, then it is defined as a multi objective linear fractional
programming problem MOLFPP in this research. The transformation characteristics are illustrated and the
solution procedure and numerical example are presented.
This document summarizes a paper about a projection-free first-order optimization method for convex problems. The method generalizes Frank-Wolfe optimization to arbitrary convex domains by solving a linearized problem at each iteration instead of a projection step. The method guarantees an epsilon duality gap within O(1/epsilon) iterations. It provides sparse or low-rank solutions to 1-norm and nuclear norm regularized problems, with sparsity or rank bounds of O(1/epsilon). Applications include support vector machines, compressed sensing, and matrix completion.
Dynamic programming is a technique for solving complex problems by breaking them down into simpler sub-problems. It involves storing solutions to sub-problems for later use, avoiding recomputing them. Examples where it can be applied include matrix chain multiplication and calculating Fibonacci numbers. For matrix chains, dynamic programming finds the optimal order for multiplying matrices with minimum computations. For Fibonacci numbers, it calculates values in linear time by storing previous solutions rather than exponentially recomputing them through recursion.
MACHINE LEARNING IS GOING TO DEFINE THE NEXT ERA; PEOPLE SAY IT WILL HAVE SIMILAR EFFECTS AS ELECTRICITY OR INTERNET HAD IN their TIMES .ARITIFICIAL INTELLIGENCE IS THE NEXT BEST THING IN THE WORLD OF TECHNOLOGY , BLOCKCHAIN AFTER THAT
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
This document contains a chapter from the Handbook of Applied Cryptography discussing number-theoretic problems relevant to cryptography. It summarizes algorithms for integer factorization, including trial division, Pollard's rho algorithm, and general number field sieve. It also covers the RSA problem, quadratic residuosity problem, computing square roots modulo n, discrete logarithm problem, and other computational problems. Permission is granted to retrieve, print, and store this chapter for personal use but not to copy or distribute it without permission.
This document discusses linear programming techniques for managerial decision making. Linear programming can determine the optimal allocation of scarce resources among competing demands. It consists of linear objectives and constraints where variables have a proportionate relationship. Essential elements of a linear programming model include limited resources, objectives to maximize or minimize, linear relationships between variables, homogeneity of products/resources, and divisibility of resources/products. The linear programming problem is formulated by defining variables and constraints, with the objective of optimizing a linear function subject to the constraints. It is then solved using graphical or simplex methods through an iterative process to find the optimal solution.
This document discusses packing problems and how to formulate and solve them as mixed integer linear programs (MILPs) using the Gurobi optimization solver. Packing problems involve fitting objects into containers in the most dense packing possible or using the fewest number of containers. The document provides examples of packing problems and presents an MILP formulation for packing rectangles. It explains why MILPs are suitable for packing problems and how to model the constraints, variables, and objective function. Finally, it outlines the basic steps for solving a packing problem MILP using Gurobi: defining the model struct, modifying parameters, running the optimization, and printing the solution.
Shor's discrete logarithm quantum algorithm for elliptic curvesXequeMateShannon
This document summarizes John Proos and Christof Zalka's research on implementing Shor's quantum algorithm for solving the discrete logarithm problem over elliptic curves. It shows that for elliptic curve cryptography, a quantum computer could solve problems beyond the capabilities of classical computers using fewer qubits than for integer factorization. Specifically, a 160-bit elliptic curve key could be broken using around 1000 qubits, compared to 2000 qubits needed to factor a 1024-bit RSA modulus. The main technical challenge is implementing the extended Euclidean algorithm to compute multiplicative inverses modulo a prime p.
This document provides a summary of key concepts in artificial intelligence, organized into the following sections:
1. Reflex-based models such as linear predictors for classification and regression using techniques like loss minimization and regularization.
2. States-based models including search optimization techniques like tree search, graph search, A* search and Markov decision processes.
3. Variables-based models covering constraint satisfaction problems, Bayesian networks and inference.
4. Logic-based models discussing knowledge bases, propositional logic and first-order logic.
The document defines important terms and algorithms at a high level across different areas of AI like supervised and unsupervised learning, neural networks, optimization, probabilistic modeling and logic.
The document provides information about linear programming, including:
- Linear programming is a technique to optimize allocation of scarce resources among competing demands. It involves determining variables, constraints, and an objective function.
- The linear programming model consists of linear objectives and constraints, where variables have a proportionate relationship (e.g. increasing labor increases output proportionately).
- Essential elements of a linear programming model include limited resources, an objective to maximize or minimize, linear relationships between variables, identical resources/products, and divisible resources.
- Linear programming problems can be solved graphically by plotting constraints and objective function to find the optimal point, or algebraically using the simplex method through iterative tables.
In this unit, you will experience the powerful impact communication .docxwhitneyleman54422
This document provides instructions for an assignment requiring students to download a template, follow the instructions in the template to complete an analysis of communication concepts relating to cultural diversity, and demonstrate their understanding through in-text citations and references in APA format.
In this task, you will write an analysis (suggested length of 3–5 .docxwhitneyleman54422
In this task, you will write an analysis (
suggested length of 3–5 pages
) of one work of literature. Choose
one
work from the list below:
Classical Period
• Sappho, “The Anactoria Poem” ca. 7th century B.C.E. (poetry)
• Aeschylus, “Song of the Furies” from
The Eumenides
, ca. 458 B.C.E. (poetry)
• Sophocles,
Antigone
, ca. 442 B.C.E. (drama)
• Aristotle, Book 1 from the
Nichomachean Ethics
, ca. 35 B.C.E. (philosophical text)
• Augustus,
The Deeds of the Divine Augustus
, ca. 14 C.E. (funerary inscription)
• Ovid, “The Transformation of Daphne into a Laurel” an excerpt from Book 1 of
The Metamorphoses
, ca. 2 C.E. (poetry)
Renaissance
• Francesco Petrarch, “The Ascent of Mount Ventoux” 1350 (letter)
• Giovanni Pico della Mirandola, the first seven paragraphs of the “Oration on the Dignity of Man” ca. 1486 (essay excerpt)
• Leonardo da Vinci, Chapter 28 “Comparison of the Arts” from
The Notebooks
ca. 1478-1518 (art text)
• Edmund Spenser, Sonnet 30, “My Love is like to Ice” from
Amoretti
1595 (poetry)
• William Shakespeare, Sonnet 18, “Shall I Compare Thee to a Summer’s Day” 1609 (poetry)
• Francis Bacon, “Of Studies” from
The Essays or Counsels…
1625 (essay)
• Anne Bradstreet, “In Honour of that High and Mighty Princess, Queen Elizabeth” 1643 (poetry)
• Andrew Marvell, “To his Coy Mistress” 1681 (poetry)
Enlightenment
• René Descartes, Part 4 from
Discourse on Method
, 1637 (philosophical text)
• William Congreve,
The Way of the World
, 1700 (drama-comedy)
• Jonathan Swift, “A Modest Proposal” 1729 (satirical essay)
• Voltaire, “Micromégas” 1752 (short story, science fiction)
• Phillis Wheatley, “To S.M., a Young African Painter, on Seeing his Works” 1773 (poetry)
• Thomas Paine, “Common Sense” 1776 (essay)
• Johann Wolfgang von Goethe, “The Fisherman” 1779 (poetry)
• Immanuel Kant, “An Answer to the Question: What is Enlightenment?” 1784 (essay)
Romanticism
• Lord Byron, “She Walks in Beauty” 1813 (poetry)
• Samuel Taylor Coleridge, “Kubla Khan” 1816 (poetry)
• Edgar Allan Poe, “The Fall of the House of Usher” 1839 (short story)
• Alexander Dumas,
The Count of Monte Cristo
, 1844 (novel)
• Emily Brontë,
Wuthering Heights
, 1847 (novel)
• Herman Melville, “Bartleby, the Scrivener: A Story of Wall-Street” 1853 (short story)
• Emily Dickinson, “A Narrow Fellow in the Grass” 1865 (poetry)
• Friedrich Nietzsche, Book 4 from
The Joyful Wisdom
, 1882 (philosophical text)
Realism
• Charles Dickens,
A Christmas Carol
, 1843 (novella)
• Karl Marx and Friedrich Engles,
The Communist Manifesto
, 1848 (political pamphlet)
• Christina Rossetti, “Goblin Market” 1862 (poetry)
• Matthew Arnold, “Dover Beach” 1867 (poetry)
• Robert Louis Stevenson,
The Strange Case of Dr. Jekyll and Mr. Hyde
, 1886 (novella)
• Kate Chopin, “The Story of an Hour” 1894 (short story)
• Mark Twain, “The.
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This document provides an overview of optimisation techniques for static and dynamic contexts. It discusses the principles of optimisation, including formulating problems with objective functions and constraints. It also covers topics like gradient vectors, Hessian matrices, unimodal/multimodal functions, and numerical methods for solving static optimisation problems. The document aims to provide an understanding of optimisation principles that can be applied to linear and nonlinear, unconstrained and constrained problems.
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This document provides instructions for an assignment requiring students to download a template, follow the instructions in the template to complete an analysis of communication concepts relating to cultural diversity, and demonstrate their understanding through in-text citations and references in APA format.
In this task, you will write an analysis (suggested length of 3–5 .docxwhitneyleman54422
In this task, you will write an analysis (
suggested length of 3–5 pages
) of one work of literature. Choose
one
work from the list below:
Classical Period
• Sappho, “The Anactoria Poem” ca. 7th century B.C.E. (poetry)
• Aeschylus, “Song of the Furies” from
The Eumenides
, ca. 458 B.C.E. (poetry)
• Sophocles,
Antigone
, ca. 442 B.C.E. (drama)
• Aristotle, Book 1 from the
Nichomachean Ethics
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• Augustus,
The Deeds of the Divine Augustus
, ca. 14 C.E. (funerary inscription)
• Ovid, “The Transformation of Daphne into a Laurel” an excerpt from Book 1 of
The Metamorphoses
, ca. 2 C.E. (poetry)
Renaissance
• Francesco Petrarch, “The Ascent of Mount Ventoux” 1350 (letter)
• Giovanni Pico della Mirandola, the first seven paragraphs of the “Oration on the Dignity of Man” ca. 1486 (essay excerpt)
• Leonardo da Vinci, Chapter 28 “Comparison of the Arts” from
The Notebooks
ca. 1478-1518 (art text)
• Edmund Spenser, Sonnet 30, “My Love is like to Ice” from
Amoretti
1595 (poetry)
• William Shakespeare, Sonnet 18, “Shall I Compare Thee to a Summer’s Day” 1609 (poetry)
• Francis Bacon, “Of Studies” from
The Essays or Counsels…
1625 (essay)
• Anne Bradstreet, “In Honour of that High and Mighty Princess, Queen Elizabeth” 1643 (poetry)
• Andrew Marvell, “To his Coy Mistress” 1681 (poetry)
Enlightenment
• René Descartes, Part 4 from
Discourse on Method
, 1637 (philosophical text)
• William Congreve,
The Way of the World
, 1700 (drama-comedy)
• Jonathan Swift, “A Modest Proposal” 1729 (satirical essay)
• Voltaire, “Micromégas” 1752 (short story, science fiction)
• Phillis Wheatley, “To S.M., a Young African Painter, on Seeing his Works” 1773 (poetry)
• Thomas Paine, “Common Sense” 1776 (essay)
• Johann Wolfgang von Goethe, “The Fisherman” 1779 (poetry)
• Immanuel Kant, “An Answer to the Question: What is Enlightenment?” 1784 (essay)
Romanticism
• Lord Byron, “She Walks in Beauty” 1813 (poetry)
• Samuel Taylor Coleridge, “Kubla Khan” 1816 (poetry)
• Edgar Allan Poe, “The Fall of the House of Usher” 1839 (short story)
• Alexander Dumas,
The Count of Monte Cristo
, 1844 (novel)
• Emily Brontë,
Wuthering Heights
, 1847 (novel)
• Herman Melville, “Bartleby, the Scrivener: A Story of Wall-Street” 1853 (short story)
• Emily Dickinson, “A Narrow Fellow in the Grass” 1865 (poetry)
• Friedrich Nietzsche, Book 4 from
The Joyful Wisdom
, 1882 (philosophical text)
Realism
• Charles Dickens,
A Christmas Carol
, 1843 (novella)
• Karl Marx and Friedrich Engles,
The Communist Manifesto
, 1848 (political pamphlet)
• Christina Rossetti, “Goblin Market” 1862 (poetry)
• Matthew Arnold, “Dover Beach” 1867 (poetry)
• Robert Louis Stevenson,
The Strange Case of Dr. Jekyll and Mr. Hyde
, 1886 (novella)
• Kate Chopin, “The Story of an Hour” 1894 (short story)
• Mark Twain, “The.
In this SLP you will identify where the major transportation modes a.docxwhitneyleman54422
In this SLP you will identify where the major transportation modes are used in the EESC from SLP3: rail, inland water, ocean steamer, and/or OTR.
There are five basic transportation modes: rail, inland water ways, ocean, over-the-road, and air. We will not be concerned about air transport in this SLP as it is the least used and most expensive in general supply chain transportation.
Review and read these resources on these three transportation modes: rail, inland water, and OTR. Ocean is not included in these readings since it is mainly used for importing and exporting. This will be covered in more detail in LOG502. But you are asked to identify where ocean transport is used, but not in detail.
RESOURCES - SEE SLP 3 RESOURCES IN BACKGROUND PAGE
Session Long Project
Review the EESC from SLP2. Identify in the EESC where each of the four modes of transportation are used: rail, inland water, ocean, and OTR. You can use topic headings for each mode. Identify the materials being transported from which industry to which industry. Discuss why this mode is being used and what the costs are on a per ton-mile basis.
SLP Assignment Expectations
The paper should include:
Background:
Briefly
review and discuss the targeted product, company, and industry
Diagram: Include the diagram of the EESC
Transportation Discussion: Discuss each of the four transportation modes (rail, inland water, ocean, OTR) in the EESC and where each one is used. Discuss why this mode is used and the costs of using.
Clarity and Organization: The paper should be well organized and clearly discuss the various topics and issues in depth and breadth.
Use of references and citations: at least six (6) proper references should be used correctly, cited in the text, and listed in the references using proper APA format.
Length: The paper should be three to four pages – the body of the paper excluding title page and references page.
NOTE: You can use the transportation resources. You should also do independent research and find at least two additional appropriate references, for a total of at least six.
SLP Resources
Waterways
American Society of Civil Engineers. (2014). Report card for America’s infrastructure.
Infrastructure Report Card.
Retrieved from
http://www.infrastructurereportcard.org/fact-sheet/inland-waterways
Texas Transportation Institute. (2009). A Modal Comparison Of Domestic Freight Transportation Effects On The General Public, retrieved from
http://www.nationalwaterwaysfoundation.org/study/FinalReportTTI.pdf
U.S. Army Corps of Engineers. (2014). The U.S. Waterway System, Transportation Facts & Information; Navigation Center. Retrieved from
http://www.navigationdatacenter.us/factcard/factcard12.pdf
Railroads
Bureau of Transportation Statistics (Rail), retrieved from
https://www.bts.gov/topics/rail
USDOT (2012). Freight rail: data & resources. Retrieved on 20 Sep 2016 from
https://www.fra.dot.gov/Page/P0365
American Association of Railroads. Ret.
In this module the student will present writing which focuses attent.docxwhitneyleman54422
In this module the student will present writing which focuses attention on himself or herself (personal writing). We will start into college composition by reading a series of essays that explore the rhetorical modes of narration and decscription. If you think about your own lives, you'll note the importance of the stories that surround you. Think of your family's story, your friends' stories, and your very own story. Think of the detail that constitute these stories, of how they engage your sense of taste, touch, sound, smell, and sight. This module will focus on how you can better craft your own story and share it with others.
Competencies Addressed in this Module:
Competency #1: The student will demonstrate an understanding of the writing process by:
Choosing and limiting a subject that can be sufficiently developed within a given time, for a specific purpose, for a specific purpose and audience.
Developing and refining pre-writing and planning skills.ormulating the main point to reflect the subject and purpose of the writing.
Formulating the main point to reflect the subject and purpose of the writing.
Supporting the main point with specific details and arranging them logically.
Writing an effective conclusion.
Competency #3: The student will demonstrate the ability to proofread, edit, and revise by:
Recognizing and correcting errors in clarity
Recognizing and correcting errors in unity and coherence.
Using conventional sentence structure and correcting sentence errors such as fragments, run-ons, comma splices, misplaced modifiers and faulty parallelism.
Recognizing and correcting errors in utilizing the conventions of Standard American English including:
Using standard verb forms and consistent tense.
Maintaining agreement between subject and verb, pronoun and antecedent.
Using proper case forms--consistent point of view.
Using standard spelling, punctuation, and capitalization.
Selecting vocabulary appropriate to audience, purpose, and occasion.
Aditional inf: I am a woma. I am 25 years old. I have a husband and a one year old son
.
In this module, we looked at a variety of styles in the Renaissa.docxwhitneyleman54422
In this module, we looked at a variety of styles in the Renaissance in Italy. Artists like Botticelli, Bellini, Michelangelo, and Bronzino all incorporated Renaissance characteristics into their works, and yet their works look different from each other.
To address form and content in the artistic developments and trends that took place in the Renaissance, look closely at examples from each of these artists.
Choose one painting by one of the artists listed above, and identify characteristics and techniques of the Renaissance style.
Then, address how the work departed from typical Renaissance formulas to become signature to that artist's particular style.
Finally, why did you select this artist? What draws you to their work?
.
In this experiential learning experience, you will evaluate a health.docxwhitneyleman54422
In this experiential learning experience, you will evaluate a healthcare plan using the attached worksheet. The selected plan can be your own health insurance or another plan.
Step 1
Use published information on the selected health insurance plan to complete the
assignment 5.1 worksheet
.
Step 2
Create a 7-10 slide Power Point presentation to include the following:
Introduction to the plan, including geographic boundaries
Major coverage inclusions and exclusions (Medical, Dental, Vision etc.)
Costs to consumer for insurance under the plan (include premiums, deductibles, copays, prescription costs)
Health insurance plan ratings if available. If no ratings are found for this plan, include a possible explanation for this situation.
Evaluation of the health insurance plan-include your evaluation of this plan from two standpoints:
a consumer-focused on costs, coverage, and ease of use
a public health nurse- focused on access to care for populations and improving health outcomes.
Cite all sources in APA format on a reference slide and with on-slide citations.
.
In this essay you should combine your practice responding and analyz.docxwhitneyleman54422
In this essay you should combine your practice responding and analyzing short stories with support derived from research. So far in class, we have practiced primarily formal analysis. Now I want you to practice "joining the conversation." In this essay you will write a literary analysis that incorporates the ideas of others. The trick is to accurately present ideas and interpretations gathered from your research while adding to the conversation by presenting
your own
ideas and analysis.
You will be evaluated based on how well you use external sources. I want to see that you can quote, paraphrase and summarize without plagiarizing. Remember, any unique idea must be credited, even if you put it in your own words.
Choose one of the approaches explained in the "Approaches to Literary Analysis" located at the bottom of this document. Each approach will require research, and that research should provide the context in which you present your own ideas and support your thesis. Be sure to properly document your research. Review the information, notes, and pamphlets I have distributed in class as these will help guide you.
While I am asking you to conduct outside research, do not lose sight of the primary text to which you are responding---the story! Your research should support
your
interpretations of the story. Be sure that your thesis is relevant to the story and that you quote generously from the story.
Purpose:
critical analysis, Argument, writing from sources
Length:
approx 1200 words
Documentation:
Minimum of 4 sources required (one primary source—the story or poem analyzed, and three secondary, peer reviewed journals). (Note: review the material in "finding and evaluating sources.ppt" to help you choose relevant and trustworthy sources.)
Choose from the following short stories:
The Lottery,
Shirley Jackson
A Rose for Emily,
William Faulkner
The Dead
, James Joyce
The Veldt
, Ray Bradbury
Hills Like White Elephants,
Ernest Hemingway
The Cask of Amontillado or The Tell-Tale Heart,
Edgar Allen Poe
Below are some examples.
They are just here to give you an idea of the type of approaches that will work for this essay.
1. Philosophical analysis: How do the stories by Jean Paul Sartre and Albert Camus reflect the philosophy of existentialism?
2. Socio/cultural analysis: What opinion about marriage and gender roles does Hemingway advance in "The Short Happy Life of Francis Macomber"?
3. Historical analysis:: What social dilemmas faced by African Americans in the 1960s might have inspired Toni Cade Bambara to write "The Lesson"?
4. Biographical analysis: What events in Salman Rushdie's life might have influenced the events in "At the Auction of the Ruby Slippers"?
5. Psychological analysis: How is John Cheever's "The Swimmer" a metaphor for the psychology of addiction?
Approaches to Literary analysis
Formal analysis
- This type of analysis focuses on the formal elements of the work (language.
In this Discussion, pick one film to write about and answer ques.docxwhitneyleman54422
In this Discussion, pick one film to write about and answer questions below the film descriptions. If it has been a while since you have seen these films, they are available through online sources and various rental outlets. Although I have provided links to some of the films, I cannot guarantee they are still operable. If the links do not work, try your own online sources.
Dances with Wolves
(1990). Lt. John Dunbar (Kevin Costner) is assigned to the Western frontier on his own request after an act of bravery. He finds himself at an abandoned outpost. At first he maintains strict order using the methods and practices taught to him by the military, but as the film progresses, he makes friends with a nearby Native American tribe, and his perceptions of the military, the frontier, and Native Americans change dramatically.
Working Girl
(1988) Tess McGill (Melanie Griffith) works as a secretary for a large firm involved in acquiring media corporations such as radio and television. When her boss has a skiing accident, Tess gets a chance to use her own ideas and research, ideas that she has been keeping within herself for years – ideas that are arguably better, and more insightful into mass media practices, than her boss’s ideas were.
Schindler’s List
(1993). In Poland during World War II, Oskar Schindler (Liam Neeson) gradually becomes concerned for his Jewish workforce after witnessing their persecution by the Nazis. He initially was motivated by profit, but as the war progressed he began to sympathize with his Jewish workers and attempted to save them. He was credited with saving over 1000 Jews from extermination. (Based on a true story.)
Gran Torino
(2008). Walt Kowalski (Clint Eastwood), a recently widowed Korean War veteran alienated from his family and angry at the world. Walt's young neighbor, an Asian American, is pressured into stealing Walt's prized 1972 Ford Gran Torino by his cousin for his initiation into a gang. Walt thwarts the theft and subsequently develops a relationship with the boy and his family.
Describe the specific theories, assumptions, or “schools of thought” that the characters in the film have. How do their schools of thought differ?
How do the main characters change over the course of a film? How do their goals or desires change? Do they see themselves differently by the end of the film?
Which reflective theory from the course best illustrates the process the main characters go through during the film? How so?
Would you say that the main characters evolved or grew after learning something that was new, or a new approach, a new theory, or a new understanding of their place in the world?
I suggest that you refrain from reiterating the plotline. Rather, stay focused on character changes and the influences on those changes. Be sure to refer to the readings; use proper citations! This discussion will be scored based on the
Grading Rubric for Discussions
Please include the name of your film in the d.
In this assignment, you will identify and interview a family who.docxwhitneyleman54422
This assignment requires students to interview a family experiencing stress from a new life event such as a baby, job change, or divorce. Students must obtain written consent from the family, agree not to publish any identifying information, and use the information only for classroom purposes. During the interview, students will gather details about the family, the history and cause of their stress, how family members responded to life events, family dynamics, strengths, coping strategies, and goals. Students will then analyze the family using research and theory, provide recommendations for support resources, and reflect on communication skills used during the interview. The final paper will be 6-8 pages following APA format.
In this assignment, you will assess the impact of health legisla.docxwhitneyleman54422
In this assignment, you will assess the impact of health legislation on nursing practice and communicate your analysis to your peers. GovTrack.us provides a list of federal health bills that are currently in process in Congressional Committees.
CO4: Integrates clinical nursing judgment using effective communication strategies with patients, colleagues, and other healthcare providers. (PO#4)
CO7: Integrates the professional role of leader, teacher, communicator, and manager of care to plan cost-effective, quality healthcare to consumers in structured and unstructured settings. (PO#7)
.
In this assignment, you will create a presentation. Select a topic o.docxwhitneyleman54422
In this assignment, you will create a presentation. Select a topic of your choice from any subject we have covered in this course.
TOPICS..
INTERNET
COMPUTERS
MOBILE AND GAME DEVICES
DATA AND INFORMATION
THE WEB
DIGITAL SECURITY AND PRIVACY
PROGRAMS AND APPS
COMMUNICATION AND NETWORKS
TECHNOLOGY USERS
THE INTERNET
GRAPHICS AND MEDIA APPLICATIONS
FILE, DISK AND SYSTEM MANAGEMENT TOOLS
PROCESSORS
CLOUD COMPUTING
ADAPTERS
POWER SUPPLY AND BATTERIES
WIRELESS SECURITY
Explain why you select this topic.
Explain why this topic is important.
Discuss the advantages and disadvantages of your select topic.
Include any other information you might thing is relative to your topic.
Your presentation should be a minimum of 15-20 slides in length. Include the title, references, images, graphics, and diagrams.
.
In this assignment, the student will understand the growth and devel.docxwhitneyleman54422
In this assignment, the student will understand the growth and development of executive leadership by looking at the dynamics between the president and Congress in the period from the founding to the Spanish-American War. In a 6–8- page paper, the student will focus on: 1) how presidents pursued international relations, 2) how presidents were able to project force, and 3) congressional restrictions on presidential actions. The student may write about the president of his/her choice.
.
In this assignment, I want you to locate two pieces of news detailin.docxwhitneyleman54422
In this assignment, I want you to locate two pieces of news detailing how an organization is responding to the COVID-19 crisis. You will turn this assignment into me via a Word Document attached to a separate email titled "extra credit assignment, Your Name" with your actual name in the subject line so I know to save the email for grading.
You need to analyze how businesses are handling the current COVID-19 crisis and I want to see if you can track down a press release from the organization, an email to their stakeholders, or even a screenshot of their website in which they explicitly address the actions they are taking in light of this new world we find ourselves in. However, the screenshots, hyperlinks to news stories, etc. are only one component of the assignment, your analysis is far and away from the more important component. Once you have tracked down two examples of how a business/organization is responding to the COVID-19 crisis, I want you to tell me how effective you perceive its action to be. Use any of the vocabulary or concepts that we have learned thus far in the semester to support your analysis. For example, is the business/organization using appropriate new media platforms to reach stakeholders? Is communication timely? Is the organization's tone sincere? What could have been done better? I am expecting one page, double-spaced for the length of your analysis, APA format. The images and or hyperlinks you compile will not be counted towards the length of your writing.
.
In this assignment worth 150 points, you will consider the present-d.docxwhitneyleman54422
In this assignment worth 150 points, you will consider the present-day relevance of history with a current event from a legitimate news source (your instructor will provide several options to choose from) and do the following: (1) summarize the article¿s main idea in a paragraph (5 sentences minimum), (2) write two paragraphs in which you utilize your textbook and notes to analyze how your current event selection relates to the past.
the topics are below, just choose one of the topic from list below..
Neanderthals and string
Neanderthals Left Africa Sooner Than We Think?
Discovery of Neanderthal Skeleton and Burial
Searching for Nefertiti
Discovery of Donkeys Used in Polo (Ancient China)
Ancient Maya Capital Found in Backyard
Long Lost Greek City Found
Ancient Roman Weapon
Viking Burial Discovery
Saving Timbuktu's Treasures
.
In the readings thus far, the text identified many early American in.docxwhitneyleman54422
In the readings thus far, the text identified many early American interests in the Middle East from geopolitical to missionary. Using the text and your own research, compare these early interests with contemporary American interests in the Middle East.
In particular, how has becoming 1) a global hegemon after WWII and 2) the concurrent process of ‘secularization’ transformed American foreign policy thought and behavior toward Israel and the Middle East region generally? What themes have remained constant and what appear new? Would you attribute changes more to America’s new geopolitical role after WWII, or to the increasing secularization of American society? Explain carefully. In 500 words
.
In the Roman Colony, leaders, or members of the court, were to be.docxwhitneyleman54422
In the Roman Colony, leaders, or members of the court, were to be:
•Local elites•Be freeborn•Between the ages of 22 – 55•Community resident•Moral integrity
From the members, two were chosen as unpaid chief magistrates (Judges). They would have to “buy into” that position, but the recognition was worth the financial output. This week's discussion prompter is:
Money alone influences others. Please analyze and critically discuss.
In your response, remember that all this is about leadership, the context which is set in Rome.
.
In the provided scenario there are a few different crimes being .docxwhitneyleman54422
In the provided scenario there are a few different crimes being committed and each could be argued multiple ways.
Steve could be charged with attempted murder. He was stabbing Michelle in the chest repeatedly. Due to the details of the scenario his charge could only be attempted because Michelle got up from the attack and charged Stacy. If she later died from her injuries Steve would/could be charged with murder. Even though he was “visibly drunk” he still maintained the purposely, knowing, or reckless intent to cause harm. He was coherent enough to make statements to her about how much he loved her, but still showed an extreme indifference to life and intent cause serious bodily harm. The biggest obstacle to a murder charge for Steve is his death. He cannot be charged with anything if he cannot be alive to defend himself. This takes care of the Steve factor.
Initially Stacy could be found guilty of murder. She knowingly and intentionally took the life of another (Steve). She also expresses an intent to kill when she stated, “I have had enough of you Steve”. From the scenario it is documented that she did not care for Steve and along with her statements, it can be shown that she was “just waiting for the opportunity” to kill Steve. In her favor is the fact that she attempted to stop Steve from harming another person. Her actions, while resulting in the death of another, were in the defense of a harmed person. She possibly saved the life of Michelle by using reasonable force to stop the stabbing.
Michelle could be charged with attempted murder as well. She stabbed Stacey in the chest while screaming, “how dare you”. She intended to cause death or serious physical injury. Again, if Stacey died from the wounds suffered, Michelle could/would be charged with murder. It could also be argued that Michelle had no malice aforethought. She was being stabbed and may not have known her actions were wrong. Her extreme circumstance clouded her reasonable decision making and all she was aware of is that her boyfriend, whom she loved, was just killed. This is unlikely but still a small possibility. Without more facts from the scenario it is difficult to fully play out all possibilities.
respond to this discussion question in 150 words no references please
.
STOP THE MEETING MADNESS HOW TO FREE UP TIME FOR ME.docxwhitneyleman54422
STOP
THE
MEETING
MADNESS
HOW TO FREE UP TIME FOR
MEANINGFUL WORK
BY LESLIE A. PERLOW, CONSTANCE NOONAN HADLEY, AND EUNICE EUN
SHARE THIS ARTICLE. HBR LINK MAKES IT EASY.
SEE PAGE 41 FOR INSTRUCTIONS.
FEATURE STOP THE MEETING MADNESS
62 HARVARD BUSINESS REVIEW JULY–AUGUST 2017
EL
EN
A
K
U
LI
KO
VA
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ET
TY
IM
A
G
ES
JULY–AUGUST 2017 HARVARD BUSINESS REVIEW 63
P
Poking fun at meetings is the stuff of Dilbert car-
toons—we can all joke about how soul-sucking and
painful they are. But that pain has real consequences
for teams and organizations. In our interviews with
hundreds of executives, in fields ranging from high
tech and retail to pharmaceuticals and consulting,
many said they felt overwhelmed by their meetings—
whether formal or informal, traditional or agile, face-
to-face or electronically mediated. One said, “I cannot
get my head above water to breathe during the week.”
Another described stabbing her leg with a pencil to
stop from screaming during a particularly torturous
staff meeting. Such complaints are supported by re-
search showing that meetings have increased in length
and frequency over the past 50 years, to the point
where executives spend an average of nearly 23 hours
a week in them, up from less than 10 hours in the
1960s. And that doesn’t even include all the impromptu
gatherings that don’t make it onto the schedule.
Much has been written about this problem, but the
solutions posed are usually discrete: Establish a clear
agenda, hold your meeting standing up, delegate
someone to attend in your place, and so on. We’ve
observed in our research and consulting that real im-
provement requires systemic change, because meet-
ings affect how people collaborate and how they get
their own work done.
Yet change of such scope is rarely considered. When
we probed into why people put up with the strain that
meetings place on their time and sanity, we found
something surprising: Those who resent and dread
meetings the most also defend them as a “necessary
evil”—sometimes with great passion. Consider this
excerpt from the corporate blog of a senior executive
in the pharmaceutical industry:
I believe that our abundance of meetings at our
company is the Cultural Tax we pay for the inclusive,
learning environment that we want to foster…
and I’m ok with that. If the alternative to more
meetings is more autocratic decision-making, less
input from all levels throughout the organization,
and fewer opportunities to ensure alignment and
communication by personal interaction, then give
me more meetings any time!
To be sure, meetings are essential for enabling col-
laboration, creativity, and innovation. They often foster
relationships and ensure proper information exchange.
They provide real benefits. But why would anyone ar-
gue in defense of excessive meetings, especially when
no one likes them much?
Because executives want to be good soldiers. When
they sacrifice their own .
Stoichiometry Lab – The Chemistry Behind Carbonates reacting with .docxwhitneyleman54422
Stoichiometry Lab – The Chemistry Behind Carbonates reacting with Vinegar
Objectives: To visually observe what a limiting reactant is.
To measure the change in mass during a chemical reaction due to loss of a gas.
To calculate CO2 loss and compare actual loss to expected CO2 loss predicted by the balanced chemical equation.
Materials needed: Note: Plan ahead as you’ll need to let Part 1 sit for at least 24 hours.
plastic beaker graduated cylinder
electronic balance 2 eggs
1 plastic cup baking soda (5 g)
dropper vinegar (500mL)
2 identical cups or glasses (at least 500 mL)
Safety considerations: Safety goggles are highly recommended for this lab as baking soda and vinegar chemicals can be irritating to the eyes. If your skin becomes irritated from contact with these chemicals, rinse with cool water for 15 minutes.
Introduction:
The reaction between baking soda and vinegar is a fun activity for young people. Most children (and adults!) enjoy watching the foamy eruption that occurs upon mixing these two household substances. The reaction has often been used for erupting volcanoes in elementary science classes. The addition of food coloring makes it even more fun. The reaction involves an acid-base reaction that produces a gas (CO2). Acid-base reactions typically involve the transfer of a hydrogen ion (H+) from the acid (HA) to the base (B−):
HA + B− --> A− + BH (eq #1)
acid base
The base often (although not always) carries a negative charge. The acid usually (although not always) becomes negatively charged through the course of the reaction because it lost an H+. An example of a typical acid base reaction is below:
HCl(aq) + NaOH(aq) --> NaCl(aq) + H2O(l) (eq #2)
The reaction is actually taking place between the hydrogen ion (H+) and the hydroxide ion (OH−). The chloride and sodium are spectator ions. To write the reaction in the same form as eq #1:
HCl(aq) + OH- --> Cl- + H2O (l) (eq #3)
Sodium bicarbonate (NaHCO3) will dissociate in water to form sodium ion (Na+) and bicarbonate ion (HCO3−).
NaHCO3 --> Na+ + HCO3− (eq #4)
Vinegar is usually a 5% solution of acetic acid in water. The bicarbonate anion (HCO3−) can act as a base, accepting a hydrogen ion from the acetic acid (HC2H3O2) in the vinegar. The Na+ is just a spectator ion and does nothing.
HCO3− + HC2H3O2 --> H2CO3 + C2H3O2− (eq#5)
Bicarbonate acetic acid carbonic acid acetate ion
The carbonic acid that is formed (H2CO3) decomposes to form water and carbon dioxide:
H2CO3 --> H2O(l) + CO2(g) (eq#6)
carbonic acid water carbon dioxide
The latter reaction (production of carbon dioxide) accounts for the bubbles and the foaming that is observed upon mixing vinegar and baki.
How to Setup Default Value for a Field in Odoo 17Celine George
In Odoo, we can set a default value for a field during the creation of a record for a model. We have many methods in odoo for setting a default value to the field.
A Visual Guide to 1 Samuel | A Tale of Two HeartsSteve Thomason
These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.pptHenry Hollis
The History of NZ 1870-1900.
Making of a Nation.
From the NZ Wars to Liberals,
Richard Seddon, George Grey,
Social Laboratory, New Zealand,
Confiscations, Kotahitanga, Kingitanga, Parliament, Suffrage, Repudiation, Economic Change, Agriculture, Gold Mining, Timber, Flax, Sheep, Dairying,
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...TechSoup
Whether you're new to SEO or looking to refine your existing strategies, this webinar will provide you with actionable insights and practical tips to elevate your nonprofit's online presence.
How to Download & Install Module From the Odoo App Store in Odoo 17Celine George
Custom modules offer the flexibility to extend Odoo's capabilities, address unique requirements, and optimize workflows to align seamlessly with your organization's processes. By leveraging custom modules, businesses can unlock greater efficiency, productivity, and innovation, empowering them to stay competitive in today's dynamic market landscape. In this tutorial, we'll guide you step by step on how to easily download and install modules from the Odoo App Store.
How to Manage Reception Report in Odoo 17Celine George
A business may deal with both sales and purchases occasionally. They buy things from vendors and then sell them to their customers. Such dealings can be confusing at times. Because multiple clients may inquire about the same product at the same time, after purchasing those products, customers must be assigned to them. Odoo has a tool called Reception Report that can be used to complete this assignment. By enabling this, a reception report comes automatically after confirming a receipt, from which we can assign products to orders.
A Free 200-Page eBook ~ Brain and Mind Exercise.pptxOH TEIK BIN
(A Free eBook comprising 3 Sets of Presentation of a selection of Puzzles, Brain Teasers and Thinking Problems to exercise both the mind and the Right and Left Brain. To help keep the mind and brain fit and healthy. Good for both the young and old alike.
Answers are given for all the puzzles and problems.)
With Metta,
Bro. Oh Teik Bin 🙏🤓🤔🥰
4. 4.6.3 Calling and Using fminunc.m to Solve Unconstrained
Problems . . . . . . . . . 39
4.7 Derivative free Optimization - direct (simplex) search
methods . . . . . . . . . . . . . . 45
1
Chapter 1
Introduction to Mathematical
Programming
1.1 A general Mathematical Programming Problem
f(x) −→ min (max)
subject to
x ∈ M.
(O)
The function f : Rn → R is called the objective function and the
5. set M ⊂ Rn is the feasible set of (O).
Based on the description of the function f and the feasible set
M, the problem (O) can be classified
as linear, quadratic, non-linear, semi-infinite, semi-definite,
multiple-objective, discrete optimization
problem etc1.
1.1.1 Some Classes of Optimization Problems
Linear Programming
If the objective function f and the defining functions of M are
linear, then (O) will be a linear
optimization problem.
General form of a linear programming problem:
c⊤ x −→ min (max)
s.t.
Ax = a
Bx ≤ b
lb ≤ x ≤ ub;
(LO)
6. i.e. f(x) = c⊤ x and M = {x ∈ Rn | Ax = a,Bx ≤ b,lb ≤ x ≤ ub}.
Under linear programming problems are such practical problems
like: linear discrete Chebychev ap-
proximation problems, transportation problems, network flow
problems,etc.
1The terminology mathematical programming is being currently
contested and many demand that problems of the form
(O) be always called mathematical optimization problems. Here,
we use both terms alternatively.
2
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7. 3
Quadratic Programming
1
2
xT Qx + q⊤ x → min
s.t.
Ax = a
Bx ≤ b
x ≥ u
x ≤ v
(QP)
Here the objective function f(x) = 12x⊤ Qx + q⊤ x is a quadratic
function, while the feasible set
M = {x ∈ Rn | Ax = a,Bx ≤ b,u ≤ x ≤ v} is defined using linear
functions.
One of the well known practical models of quadratic
optimization problems is the least squares ap-
8. proximation problem; which has applications in almost all fields
of science.
Non-linear Programming Problem
The general form of a non-linear optimization problem is
f (x) −→ min (max)
subject to
equality constraints: gi (x) = 0, i ∈ {1, 2, . . . ,m}
inequality constraints: gj (x) ≤ 0, j ∈ {m + 1,m + 2, . . . ,m + p}
box constraints: uk ≤ xk ≤ vk, k = 1, 2, . . . ,n;
(NLP)
where, we assume that all the function are smooth, i.e. the
functions
f, gl : U −→ R l = 1, 2, . . . ,m + p
are sufficiently many times differentiable on the open subset U
of Rn. The feasible set of (NLP) is
given by
9. M = {x ∈ Rn | gi(x) = 0, i = 1, 2, . . . ,m; gj (x) ≤ 0,j = m + 1,m
+ 2, . . . ,m + p} .
We also write the (NLP) in vectorial notation as
f (x) → min (max)
h (x) = 0
g (x) ≤ 0
u ≤ x ≤ v.
Problems of the form (NLP) arise frequently in the numerical
solution of control problems, non-linear
approximation, engineering design, finance and economics,
signal processing, etc.
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4
10. Semi-infinite Programming
f(x) → min
s.t.
G(x,y) ≤ 0,∀ y ∈ Y ;
hi(x) = 0, i = 1, . . . ,p;
gj (x) ≤ 0,j = 1, . . . ,q;
x ∈ Rn;
Y ⊂ Rm.
(SIP)
Here, f,hi,gj : R
n → R, i ∈ {1, . . . ,p},j ∈ {1, . . . ,q} are smooth functions; G :
Rn × Rm → R is such
that, for each fixed y ∈ Y , G(·,y) : Rn → R is smooth and, for
each fixed x ∈ Rn,G(x, ·) : Rm → R is
smooth; furthermore, Y is a compact subset of Rm. Sometimes,
the set Y can also be given as
Y = {y ∈ Rm | uk(y) = 0,k = 1, . . . ,s1; vl(y) ≤ 0, l = 1, . . . ,s2}
11. with smooth functions uk,vl : R
m → R,k ∈ {1, . . . ,s1}, l ∈ {1, . . . ,s2}.
The problem (SIP) is called semi-infinite, since its an
optimization problem with finite number of vari-
ables (i.e. x ∈ Rn) and infinite number of constraints (i.e.
G(x,y) ≤ 0,∀ y ∈ Y ).
One of the well known practical models of (SIP) is the
continuous Chebychev approximation problem.
This approximation problem can be used for the approximation
of functions by polynomials, in filter
design for digital signal processing, spline approximation of
robot trajectory
Multiple-Objective Optimization
A multiple objective Optimization problem has a general form
min(f1(x),f1(x), . . . ,fm(x))
s.t.
12. x ∈ M;
(MO)
where the functions fk : R
n → R,k = 1, . . . ,m are smooth and the feasible set M is
defined in terms of
linear or non-linear functions. Sometimes, this problem is also
alternatively called multiple-criteria,
vector optimization, goal attainment or multi-decision analysis
problem. It is an optimization
problem with more than one objective function (each such
objective is a criteria). In this sense,
(LO),(QP)(NLO) and (SIP) are single objective (criteria)
optimization problems. If there are only two
objective functions in (MO), then (MO) is commonly called to
be a bi-criteria optimization problem.
Furthermore, if each of the functions f1, . . . ,fm are linear and
M is defined using linear functions,
13. then (MO) will be a linear multiple-criteria optimization
problem; otherwise, it is non-linear.
For instance, in a financial application we may need, to
maximize revenue and minimize risk at the
same time, constrained upon the amount of our investment.
Several engineering design problems can
also be modeled into (MO). Practical problems like autonomous
vehicle control, optimal truss design,
antenna array design, etc are very few examples of (MO).
In real life we may have several objectives to arrive at. But,
unfortunately, we cannot satisfy all
our objectives optimally at the same time. So we have to find a
compromising solution among all
our objectives. Such is the nature of multiple objective
optimization. Thus, the minimization (or
14. 5
maximization) of several objective functions can not be done in
the usual sense. Hence, one speaks
of so-called efficient points as solutions of the problem. Using
special constructions involving the
objectives, the problem (MO) can be reduced to a problem with
a single objective function.
1.1.2 Functions of the Matlab Optimization Toolbox
Linear and Quadratic Minimization problems.
linprog - Linear programming.
quadprog - Quadratic programming.
Nonlinear zero finding (equation solving).
fzero - Scalar nonlinear zero finding.
fsolve - Nonlinear system of equations solve (function solve).
15. Linear least squares (of matrix problems).
lsqlin - Linear least squares with linear constraints.
lsqnonneg - Linear least squares with nonnegativity constraints.
Nonlinear minimization of functions.
fminbnd - Scalar bounded nonlinear function minimization.
fmincon - Multidimensional constrained nonlinear
minimization.
fminsearch - Multidimensional unconstrained nonlinear
minimization, by Nelder-Mead direct
search method.
fminunc - Multidimensional unconstrained nonlinear
minimization.
fseminf - Multidimensional constrained minimization, semi-
infinite constraints.
Nonlinear least squares (of functions).
16. lsqcurvefit - Nonlinear curvefitting via least squares (with
bounds).
lsqnonlin - Nonlinear least squares with upper and lower
bounds.
Nonlinear minimization of multi-objective functions.
fgoalattain - Multidimensional goal attainment optimization
fminimax - Multidimensional minimax optimization.
Sou Ying
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Chapter 2
Linear Programming Problems
2.1 Linear programming with MATLAB
For the linear programming problem
17. c⊤ x −→ min
s.t.
Ax ≤ a
Bx = b
lb ≤ x ≤ ub;
(LP)
MATLAB: The program linprog.m is used for the minimization
of problems of the form (LP).
Once you have defined the matrices A, B, and the vectors
c,a,b,lb and ub, then you can call linprog.m
to solve the problem. The general form of calling linprog.m is:
[x,fval,exitflag,output,lambda]=linprog(f,A,a,B,b,lb,ub,x0,optio
ns)
Input arguments:
c coefficient vector of the objective
A Matrix of inequality constraints
18. a right hand side of the inequality constraints
B Matrix of equality constraints
b right hand side of the equality constraints
lb,[ ] lb ≤ x : lower bounds for x, no lower bounds
ub,[ ] x ≤ ub : upper bounds for x, no upper bounds
x0 Startvector for the algorithm, if known, else [ ]
options options are set using the optimset funciton, they
determine what algorism to use,etc.
Output arguments:
x optimal solution
fval optimal value of the objective function
exitflag tells whether the algorithm converged or not, exitflag >
0 means convergence
output a struct for number of iterations, algorithm used and
PCG iterations(when LargeScale=on)
19. lambda a struct containing lagrange multipliers corresponding
to the constraints.
6
7
Setting Options
The input argument options is a structure, which contains
several parameters that you can use with
a given Matlab optimization routine.
For instance, to see the type of parameters you can use with the
linprog.m routine use
>>optimset(’linprog’)
Then Matlab displays the fileds of the structure options.
Accordingly, before calling linprog.m you
20. can set your preferred parameters in the options for linprog.m
using the optimset command as:
>>options=optimset(’ParameterName1’,value1,’ParameterName
2’,value2,...)
where ’ParameterName1’,’ParameterName2’,... are those you
get displayed when you use
optimset(’linprog’). And value1, value2,... are their
corresponding values.
The following are parameters and their corresponding values
which are frequently used with linprog.m:
Parameter Possible Values
’LargeScale’ ’on’,’off’
’Simplex’ ’on’,’off’
’Display’ ’iter’,’final’,’off’
’Maxiter’ Maximum number of iteration
21. ’TolFun’ Termination tolerance for the objective function
’TolX’ Termination tolerance for the iterates
’Diagnostics’ ’on’ or ’off’ (when ’on’ prints diagnostic
information about the objective function)
Algorithms under linprog
There are three type of algorithms that are being implemented
in the linprog.m:
• a simplex algorithm;
• an active-set algorithm;
• a primal-dual interior point method.
The simplex and active-set algorithms are usually used to solve
medium-scale linear programming
problems. If any one of these algorithms fail to solve a linear
programming problem, then the problem
at hand is a large scale problem. Moreover, a linear
22. programming problem with several thousands of
variables along with sparse matrices is considered to be a large-
scale problem. However, if coefficient
matrices of your problem have a dense matrix structure, then
linprog.m assumes that your problem
is of medium-scale.
By default, the parameter ’LargeScale’ is always ’on’. When
’LargeScale’ is ’on’, then linprog.m
uses the primal-dual interior point algorithm. However, if you
want to set if off so that you can solve
a medium scale problem , then use
>>options=optimset(’LargeScale’,’off’)
8
In this case linprog.m uses either the simplex algorithm or the
23. active-set algorithm. (Nevertheless,
recall that the simplex algorithm is itself an active-set strategy).
If you are specifically interested to use the active set algorithm,
then you need to set both the param-
eters ’LargeScale’ and ’Simplex’, respectively, to ’off’:
>>options=optimset(’LargeScale’,’off’,’Simplex’,’off’)
Note: Sometimes, even if we specified ’LargeScale’ to be ’off’,
when a linear programming problem
cannot be solved with a medium scale algorithm, then linprog.m
automatically switches to the large
scale algorithm (interior point method).
2.2 The Interior Point Method for LP
Assuming that the simplex method already known, we find this
section a brief discussion on the
primal-dual interior point method for (LP).
24. Let A ∈ Rm×n,a ∈ Rm,B ∈ Rp×n,b ∈ Rp. Then, for the linear
programming problem
c⊤ x −→ min
s.t.
Ax ≤ a
Bx = b
lb ≤ x ≤ ub;
(LP)
if we set x̃ = x− lb we get
c⊤x̃− c⊤ lb −→ min
s.t.
Ax̃ ≤ a−A(lb)
Bx̃ = b−B(lb)
0 ≤ x̃ ≤ ub− lb;
(LP)
Now, by adding slack variables y ∈ Rm and s ∈ Rn (see below),
we can write (LP) as
25. c⊤x̃−c⊤ lb −→ min
s.t.
Ax̃ +y = a−A(lb)
Bx̃ = b−B(lb)
x̃ +s = ub− lb
x̃ ≥ 0, y ≥ 0, s ≥ 0.
(LP)
Thus, using a single matrix for the constraints, we have
c⊤x̃− c⊤ lb −→ min
A Im Om×n
B Op×m Op×n
In On×n In
26. x̃
y
s
a−A(lb)
b−B(lb)
ub− lb
x̃ ≥ 0,y ≥ 0,s ≥ 0.
9
Since, a constant in the objective does not create a difficulty,
we assume w.l.o.g that we have a problem
27. of the form
c⊤ x −→ min
s.t.
Ax = a
x ≥ 0.
(LP’)
In fact, when you call linprog.m with the original problem (LP),
this transformation will be done by
Matlab internally. The aim here is to briefly explain the
algorithm used, when you set the LargeScale
parameter to ’on’ in the options of linprog.
Now the dual of (LP’) is the problem
b⊤ w −→ max
s.t.
A⊤ w ≤ c
w ∈ Rm.
(LPD)
28. Using a slack variable s ∈ Rn we have
b⊤ w −→ max
s.t.
A⊤ w + s = c
w ∈ Rm, s ≥ 0 .
(LPD)
The problem (LP’) and (LPD) are called primal-dual pairs.
Optimality Condition
It is well known that a vector (x∗ ,w∗ ,s∗ ) is a solution of the
primal-dual if and only if it satisfies the
Karush-Kuhn-Tucker (KKT) optimlaity condition. The KKT
conditions here can be written as
A⊤ w + s = c
Ax = a
xisi = 0, i = 1, . . . ,n(Complemetarity conditions)
29. (x,y) ≥ 0.
This system can be written as
F(x,w,s) =
A⊤ w + s− c
Ax−a
XSe
(x,s) ≥ 0, (2.2)
where X = diag(x1,x2, . . . ,xn),S = diag(s1,s2, . . . ,sn) ∈ R
n×n,e = (1, 1, . . . , 1)⊤ ∈ Rn.
Primal-dual interior point methods generate iterates (xk,wk,sk)
that satisfy the system (2.1) & (2.2)
so that (2.2) is satisfied strictly; i.e. xk > 0,sk > 0. That is, for
each k, (xk,sk) lies in the interior
of the nonnegative-orthant. Thus the naming of the method as
30. interior point method. Interior point
methods use a variant of the Newton method for the system
(2.1) & (2.2).
10
Central Path
Let τ > 0 be a parameter. The central path is a curve C which is
the set of all points (x(τ),w(τ),s(τ)) ∈
C that satisfy the parametric system :
A⊤ w + s = c,
Ax = b,
xsi = τ,i = 1, . . . ,n
(x,s) > 0.
This implies C is the set of all points (x(τ),w(τ),s(τ)) that
satisfy
31. F(x(τ),w(τ),s(τ)) =
0
0
τe
Obviously, if we let τ ↓ 0, the the system (2.3) goes close to the
system (2.1) & (2.2).
Hence, theoretically, primal-dual algorithms solve the system
J(x(τ),w(τ),s(τ))
△x(τ)
△w(τ)
△s(τ)
32. 0
0
−XSe + τe
to determine a search direction (△x(τ),△w(τ),△s(τ)), where
J(x(τ),w(τ),s(τ)) is the Jacobian of
F(x(τ),w(τ),s(τ)). And the new iterate will be
(x+(τ),w+(τ),s+(τ)) = (x(τ),w(τ),s(τ)) + α(△x(τ),△w(τ),△s(τ)),
where α is a step length, usually α ∈ (0, 1], chosen in such a
way that (x+(τ),w+(τ),s+(τ) ∈ C.
However, practical primal-dual interior point methods use τ =
33. σµ, where σ ∈ [0, 1] is a constant and
µ =
x⊤ s
n
The term x⊤ s is the duality gap between the primal and dual
problems. Thus, µ is the measure of
the (average) duality gap. Note that, in general, µ ≥ 0 and µ = 0
when x and s are primal and dual
optimal, respectively.
Thus the Newton step (△x(µ),△w(µ),△s(µ)) is determined by
solving:
On A
⊤ In
A On×m Om×n
S On×m X
34. △x(τ)
△w(τ)
△s(τ)
0
0
−XSe + σµe
The Newton step (△x(µ),△w(µ),△s(µ)) is also called centering
direction that pushes the iterates
(x+(µ),w+(µ),s+(µ) towards the central path C along which the
35. algorithm converges more rapidly.
The parameter σ is called the centering parameter. If σ = 0, then
the search direction is known to
be an affine scaling direction.
Primal-Dual Interior Point Algorithm
11
Step 0: Start with (x0,w0,s0) with (x0,s0) > 0, k = 0
Step k: choose σk ∈ [0, 1], set µk = (x
k)⊤ sk/n and solve
On A
⊤ In
A On×m Om×n
S On×m X
37. (xk+1,wk+1,sk+1) ← (xk,wk,sk) + αk(△x
k,△wk,△sk)
choosing αk ∈ [0, 1] so that (x
k+1,sk+1) > 0.
If (convergence) STOP else set k ← k + 1 GO To Step k.
The Matlab LargeSclae option of linprog.m uses a predicator-
corrector like method of Mehrotra to
guarantee that (xk,sk) > 0 for each k,k = 1, 2, . . .
Predicator Step: A search direction (a predicator step) dkp =
(△x
k,△wk,△sk) is obtained by solving
the non-parameterized system (2.1) & (2.2).
Corrector Step: For a centering parameter σ is obtained from
dkc = [F
⊤(xk,wk,sk)]−1F(xk + ⊤xk,wk⊤wk,sk + ⊤sk) −σê
38. where ê ∈ Rn+m+n, whose last n components are equal to 1.
Iteration: for a step length α ∈ (0, 1]
(xk+1,wk+1,sk+1) = (xk,wk,sk) + α(dkp + d
k
c ).
2.3 Using linprog to solve LP’s
2.3.1 Formal problems
1. Solve the following linear optimization problem using
linprog.m.
2x1+ 3x2 → max
s.t.
x1+ 2x2 ≤ 8
2x1+ x2 ≤ 10
x2 ≤ 3
x1, x2 ≥ 0
For this problem there are no equality constraints and box
39. constraints, i.e. B=[],b=[],lb=[] and
ub=[]. Moreover,
>>c=[-2,-3]’; % linprog solves minimization problems
>>A=[1,2;2,1;0,1];
>>a=[8,10,3]’;
>>options=optimset(’LargeScale’,’off’);
12
i) If you are interested only on the solution, then use
>>xsol=linprog(c,A,b,[],[],[],[],[],options)
ii) To see if the algorithm really converged or not you need to
access the exit flag through:
>>[xsol,fval,exitflag]=linprog(c,A,a,[],[],[],[],[],options)
40. iii) If you need the Lagrange multipliers you can access them
using:
>>[xsol,fval,flag,output,LagMult]=linprog(c,A,a,[],[],[],[],[],opt
ions)
iv) To display the iterates you can use:
>>xsol=linprog(c,A,a,[],[],[],[],[],optimset(’Display’,’iter’))
2. Solve the following LP using linprog.m
c⊤ x −→ max
Ax = a
Bx ≥ b
Dx ≤ d
lb ≤ x ≤ lu
where
(A|a) =
(
1 1 1 1 1 1
44. 3
−4
5
−6
.
When there are large matrices, it is convenient to write m files.
Thus one possible solution will
be the following:
function LpExa2
A=[1,1,1,1,1,1;5,0,-3,0,1,0]; a=[10,15]’;
B1=[1,2,3,0,0,0; 0,1,2,3,0,0;... 0,0,1,2,3,0;0,0,0,1,2,3];
b1=[5,7,8,8];b1=b1(:);
D=[3,0,0,0,-2,1;0,4,0,-2,0,3]; d=[5,7]; d=d(:);
46. fprintf(’%s %s n’, ’Algorithm Used: ’,output.algorithm);
fprintf(’%s’,’Reason for termination:’)
if (exitflag)
fprintf(’%s n’,’ Convergence.’);
else
fprintf(’%s n’,’ No convergence.’);
end
Observe that for the problem above the simplex algorithm does
not work properly. Hence,
linprog.m uses automatically the interior point method.
2.3.2 Approximation of discrete Data by a Curve
Solve the following discrete approximation problem and plot the
approximating curve.
47. Suppose the measurement of a real process over a 24 hours
period be given by the following table
with 14 data values:
i 1 2 3 4 5 6 7 8 9 10 11 12 13 14
ti 0 3 7 8 9 10 12 14 16 18 19 20 21 23
ui 3 5 5 4 3 6 7 6 6 11 11 10 8 6
The values ti represent time and ui’s are measurements.
Assuming there is a mathematical connection
between the variables t and u, we would like to determine the
coefficients a,b,c,d,e ∈ R of the
function
u(t) = at4 + bt3 + ct2 + dt + e
so that the value of the function u(ti) could best approximate
the discrete value ui at ti, i = 1, . . . , 14
in the Chebychev sense. Hence, we need to solve the Chebyshev
approximation problem
(CA)
48. maxi=1,...,14
∣ ∣ ui −
(
at4i + bt
3
i + ct
2
i + dti + e
)∣ ∣ → min
s.t. a,b,c,d,e ∈ R