A new method namely, objective separable method based on simplex method is proposed for
finding an optimal solution to a quadratic programming problem in which the objective function can be
factorized into two linear functions. The solution procedure of the proposed method is illustrated with the
numerical example.
Optimum Solution of Quadratic Programming Problem: By Wolfe’s Modified Simple...IJLT EMAS
In this paper, an alternative approach to the Wolfe’s
method for Quadratic Programming is suggested. Here we
proposed a new approach based on the iterative procedure for
the solution of a Quadratic Programming Problem by Wolfe’s
modified simplex method. The method sometimes involves less or
at the most an equal number of iteration as compared to
computational procedure for solving NLPP. We observed that
the rule of selecting pivot vector at initial stage and thereby for
some NLPP it takes more number of iteration to achieve
optimality. Here at the initial step we choose the pivot vector on
the basis of new rules described below. This powerful technique
is better understood by resolving a cycling problem.
Quadratic Programming : KKT conditions with inequality constraintsMrinmoy Majumder
In the case of Quadratic Programming for optimization, the objective function is a quadratic function. One of the techniques for solving quadratic optimization problems is KKT Conditions which is explained with an example in this tutorial.
The PPT covered the distinguish between discrete and continuous distribution. Detailed explanation of the types of discrete distributions such as binomial distribution, Poisson distribution & Hyper-geometric distribution.
On the Numerical Solution of Differential EquationsKyle Poe
Report written to satisfy requirements of ENGR 219, Numerical Methods, as part of an independent study of the course. Topics range from multistep methods for ODE solution to finite element methods.
Optimum Solution of Quadratic Programming Problem: By Wolfe’s Modified Simple...IJLT EMAS
In this paper, an alternative approach to the Wolfe’s
method for Quadratic Programming is suggested. Here we
proposed a new approach based on the iterative procedure for
the solution of a Quadratic Programming Problem by Wolfe’s
modified simplex method. The method sometimes involves less or
at the most an equal number of iteration as compared to
computational procedure for solving NLPP. We observed that
the rule of selecting pivot vector at initial stage and thereby for
some NLPP it takes more number of iteration to achieve
optimality. Here at the initial step we choose the pivot vector on
the basis of new rules described below. This powerful technique
is better understood by resolving a cycling problem.
Quadratic Programming : KKT conditions with inequality constraintsMrinmoy Majumder
In the case of Quadratic Programming for optimization, the objective function is a quadratic function. One of the techniques for solving quadratic optimization problems is KKT Conditions which is explained with an example in this tutorial.
The PPT covered the distinguish between discrete and continuous distribution. Detailed explanation of the types of discrete distributions such as binomial distribution, Poisson distribution & Hyper-geometric distribution.
On the Numerical Solution of Differential EquationsKyle Poe
Report written to satisfy requirements of ENGR 219, Numerical Methods, as part of an independent study of the course. Topics range from multistep methods for ODE solution to finite element methods.
This presentation gives a brief idea about Interpolation. Methods of interpolating with equally/unequally spaced intervals. Please note that not all the methods are being covered in this presentation. Topics like extrapolation and inverse interpolation have also been kept aside for another ppt.
New approach for wolfe’s modified simplex method to solve quadratic programmi...eSAT Journals
Abstract
In this paper, an alternative method for Wolfe’s modified simplex method is introduced. This method is easy to solve quadratic programming problem (QPP) concern with non-linear programming problem (NLPP). In linear programming models, the characteristic assumption is the linearity of the objective function and constraints. Although this assumption holds in numerous practical situations, yet we come across many situations where the objective function and some or all of the constraints are non-linear functions. The non-linearity of the functions makes the solution of the problem much more involved as compared to LPPs and there is no single algorithm like the simplex method, which can be employed to solve efficiently all NPPs.
Keywords: Quadratic programming problem, New approach, Modified simplex method, and Optimal solution.
Here we focuses on Fixed-Point Iterative Technique for solving nonlinear Equations in Numerical Analysis. It is one of the opened-iterative techniques for finding roots called Fixed-Point of Non-linear Equations.
This presentation gives a brief idea about Interpolation. Methods of interpolating with equally/unequally spaced intervals. Please note that not all the methods are being covered in this presentation. Topics like extrapolation and inverse interpolation have also been kept aside for another ppt.
New approach for wolfe’s modified simplex method to solve quadratic programmi...eSAT Journals
Abstract
In this paper, an alternative method for Wolfe’s modified simplex method is introduced. This method is easy to solve quadratic programming problem (QPP) concern with non-linear programming problem (NLPP). In linear programming models, the characteristic assumption is the linearity of the objective function and constraints. Although this assumption holds in numerous practical situations, yet we come across many situations where the objective function and some or all of the constraints are non-linear functions. The non-linearity of the functions makes the solution of the problem much more involved as compared to LPPs and there is no single algorithm like the simplex method, which can be employed to solve efficiently all NPPs.
Keywords: Quadratic programming problem, New approach, Modified simplex method, and Optimal solution.
Here we focuses on Fixed-Point Iterative Technique for solving nonlinear Equations in Numerical Analysis. It is one of the opened-iterative techniques for finding roots called Fixed-Point of Non-linear Equations.
Probabilistic programming is a new approach to machine learning and data science that is currently the focus of intense academic research, including an ongoing DARPA program. If successful, probabilistic programming systems will allow sophisticated predictive models to be written by a wide range of domain experts. Before we get to the promised land, though, some basic challenges need to be addressed, including performance on real-world datasets, programming tools support, and education.
it contains the detail information about Dynamic programming, Knapsack problem, Forward / backward knapsack, Optimal Binary Search Tree (OBST), Traveling sales person problem(TSP) using dynamic programming
Isolation and Identification High-Biological Activity Bacteria in Yogurt Qua...IJMER
Six strains of lactic bacteria and seven strains of acetic bacteria which were isolated from
fermented food. The screening secured one strain of lactic acid bacterium LB4 which carried strong
probiotic activity and one strain of acetic acid bacterium AB7 which was capable to generate high
glucuronic acid. Activities of probiotic and glucuronic acid were useful biological activities for health
protection and enhancing. The results of DNA sequencing showed LB4 was similar to Lactobacillus
acidophilus and AB7 was similar to Gluconacetobacter nataicola with 100% of similar proportion. Both
of these bacteria were safe that could be used in food fermentation.Six strains of lactic bacteria and seven strains of acetic bacteria which were isolated from
fermented food. The screening secured one strain of lactic acid bacterium LB4 which carried strong
probiotic activity and one strain of acetic acid bacterium AB7 which was capable to generate high
glucuronic acid. Activities of probiotic and glucuronic acid were useful biological activities for health
protection and enhancing. The results of DNA sequencing showed LB4 was similar to Lactobacillus
acidophilus and AB7 was similar to Gluconacetobacter nataicola with 100% of similar proportion. Both
of these bacteria were safe that could be used in food fermentation.
Experimental Investigation of Twin Cylinder Diesel Engine Using Diesel & Met...IJMER
In view of increasing pressure on crude oil reserves and environmental degradation as an
outcome, fuels like methanol may present a sustainable solution as it can be produced from a wide
range of carbon based feedstock. The present investigation evaluates methanol as a diesel engine fuel.
The objectives of this report is to analyze the fuel consumption and the emission characteristic of a
twin cylinder diesel engine that are using Methanol & compared to usage of ordinary diesel that are
available in the market. This report describes the setups and the procedures for the experiment which
is to analyze the emission characteristics and fuel consumption of diesel engine due to usage of the
both fuels. Detail studies about the experimental setup and components have been done before the
experiment started. Data that are required for the analysis is observed from the experiments.
Calculations and analysis have been done after all the required data needed for the thesis is obtained.
The experiment used diesel engine with no load which means no load exerted on it. A four stroke Twin
cylinder diesel engine was adopted to study the brake thermal efficiency, brake specific energy
consumption, and emissions at zero load & full load with the fuel of methanol. In this study, the diesel
engine was tested using 100% methanol. By the end of the report, the successful of the project have
been started which is Diesel engine is able to run with Methanol but the engine needs to run by using
diesel fuel first, then followed by methanol and finished with diesel fuel as the last fuel usage before the
engine turned off. The performance of the engine using Methanol fuel compared to the performance of
engine with diesel fuel. Experimental results of Methanol and Diesel fuel are also compared.
Prediction of groundwater quality in Selected Locations in Imo StateIJMER
The prediction of groundwater quality in selected locations was carried out in Owerri-West
L.G.A. of Imo State. The Physical, chemical and biological parameters of groundwater samples from
Nekede (Ward A), Ihiagwa (Ward B), Eziobodo (Ward C), Obinze (Ward D) and Avu (Ward E) were
analysed using the Atomic Absorption Spectrophotometer (AAS). A total of three replicates of fifteen
different borehole water samples were collected based on distances from closest potential sources of
contamination. All parameters were detected up to 61m from pollution source and most of them
increased in concentration during the periods, pointing to infiltrations from storm water. The results
for Iron, pH and TVC decreased as distance increases while for nitrate and BOD increased as distance
increases. Results also showed that most of the boreholes were polluted and not suitable for human
consumption without adequate treatment, Regular monitoring of groundwater quality, abolishment of
unhealthy waste disposal practices and introduction of modern techniques are recommended.
Remote Access and Dual Authentication for Cloud StorageIJMER
Cloud computing is an emerging technology, which provides services over internet such as
software, hardware, network and storage. The key role for cloud computing is virtualization which
reduces the total cost and gives reliable, flexible and secured services. However compute service are
chosen between the providers located in multiple data centres. One of the major security concerns
related to the virtualization and the Storage where the outside attackers can use the files in the storage
and the data owners are not capable of knowing attacks. In this paper we proposed a high level
authentication for the cloud user and remote monitor controlled of your cloud storage. Here our model
provides the dual authentication for the cloud and to get the runtime record of the logs and the secured
application controls, the logs are remotely accessed and controlled by the owner of the data.
A helicopter is an aircraft that is lifted and propelled by one or more horizontal rotors, each
consisting of two or more rotor blades. The main objective of this seminar topic is to study the basic
concepts of helicopter aerodynamics. The forces acting on helicopter i.e. lift, drag, thrust and weight
are considered for developing analytic equations. The main topics that are discussed include blade
motions like blade flapping, feathering and lead-lag. The effect of stall on helicopter blade flapping is
studied and it was noticed that there is a sudden lift drop at this stall condition. It was also found that
dynamic stall occurs due to rapidly changing angle of attack, which inturn affect the air flow over the
airfoil. Blade flapping angle and induced angle of attack are the main parameters concerned with stall.
The theory behind blade element analysis has been inferred in detail. The importance of all these in the
present scenario are also taken into consideration
Acquisition of Long Pseudo Code in Dsss SignalIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
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.
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)
Paper Publications
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Comparative Study of the Effect of Different Collocation Points on Legendre-C...IOSR Journals
We seek to explore the effects of three basic types of Collocation points namely points at zeros of Legendre polynomials, equally-spaced points with boundary points inclusive and equally-spaced points with boundary point non-inclusive. Established in literature is the fact that type of collocation point influences to a large extent the results produced via collocation method (using orthogonal polynomials as basis function). We
analyse the effect of these points on the accuracy of collocation method of solving second order BVP. For equally-spaced points we further consider the effect of including the boundary points as collocation points. Numerical results are presented to depict the effect of these points and the nature of problem that is best handled by each.
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.
A Study on Translucent Concrete Product and Its Properties by Using Optical F...IJMER
- Translucent concrete is a concrete based material with light-transferring properties,
obtained due to embedded light optical elements like Optical fibers used in concrete. Light is conducted
through the concrete from one end to the other. This results into a certain light pattern on the other
surface, depending on the fiber structure. Optical fibers transmit light so effectively that there is
virtually no loss of light conducted through the fibers. This paper deals with the modeling of such
translucent or transparent concrete blocks and panel and their usage and also the advantages it brings
in the field. The main purpose is to use sunlight as a light source to reduce the power consumption of
illumination and to use the optical fiber to sense the stress of structures and also use this concrete as an
architectural purpose of the building
Developing Cost Effective Automation for Cotton Seed DelintingIJMER
A low cost automation system for removal of lint from cottonseed is to be designed and
developed. The setup consists of stainless steel drum with stirrer in which cottonseeds having lint is mixed
with concentrated sulphuric acid. So lint will get burn. This lint free cottonseed treated with lime water to
neutralize acidic nature. After water washing this cottonseeds are used for agriculter purpose
Study & Testing Of Bio-Composite Material Based On Munja FibreIJMER
The incorporation of natural fibres such as munja fiber composites has gained
increasing applications both in many areas of Engineering and Technology. The aim of this study is to
evaluate mechanical properties such as flexural and tensile properties of reinforced epoxy composites.
This is mainly due to their applicable benefits as they are light weight and offer low cost compared to
synthetic fibre composites. Munja fibres recently have been a substitute material in many weight-critical
applications in areas such as aerospace, automotive and other high demanding industrial sectors. In
this study, natural munja fibre composites and munja/fibreglass hybrid composites were fabricated by a
combination of hand lay-up and cold-press methods. A new variety in munja fibre is the present work
the main aim of the work is to extract the neat fibre and is characterized for its flexural characteristics.
The composites are fabricated by reinforcing untreated and treated fibre and are tested for their
mechanical, properties strictly as per ASTM procedures.
Hybrid Engine (Stirling Engine + IC Engine + Electric Motor)IJMER
Hybrid engine is a combination of Stirling engine, IC engine and Electric motor. All these 3 are
connected together to a single shaft. The power source of the Stirling engine will be a Solar Panel. The aim of
this is to run the automobile using a Hybrid engine
Fabrication & Characterization of Bio Composite Materials Based On Sunnhemp F...IJMER
The present day technology demands eco-friendly developments. In this era the
composite material are playing a vital roal in different field of Engineering .The composite materials
are using as a principle materials. Nowaday the composite materials are utilizing as a important
component of engineering field .Where as the importance of the applications of composites is well
known, but thrust on the use of natural fibres in it for reinforcement has been given priority for some
times. But changing from synthetic fibres to natural fibres provides only half green-composites. A
partial green composite will be achieved if the matrix component is also eco-friendly. Keeping this in
view, a detailed literature surveyed has been carried out through various issues of the Journals
related to this field. The material systems used are sunnhemp fibres. Some epoxy and hardener has
been also added for stability and drying of the bio-composites. Various graphs and bar-charts are
super-imposed on each other for comparison among themselves and Graphs is plotted on MAT LAB
and ORIGIN 6.0 software. To determining tensile strengths, Various properties for different biocomposites
have been compared among themselves. Comparison of the behaviour of bio-composites of
this work has been also compare with other works. The bio-composites developed in this work are
likely to get applications in fall ceilings, partitions, bio-degradable packagings, automotive interiors,
sports things (e.g. rackets, nets, etc.), toys etc.
Geochemistry and Genesis of Kammatturu Iron Ores of Devagiri Formation, Sandu...IJMER
The Greenstone belts of Karnataka are enriched in BIFs in Dharwar craton, where Iron
formations are confined to the basin shelf, clearly separated from the deeper-water iron formation that
accumulated at the basin margin and flanking the marine basin. Geochemical data procured in terms of
major, trace and REE are plotted in various diagrams to interpret the genesis of BIFs. Al2O3, Fe2O3 (T),
TiO2, CaO, and SiO2 abundances and ratios show a wide variation. Ni, Co, Zr, Sc, V, Rb, Sr, U, Th,
ΣREE, La, Ce and Eu anomalies and their binary relationships indicate that wherever the terrigenous
component has increased, the concentration of elements of felsic such as Zr and Hf has gone up. Elevated
concentrations of Ni, Co and Sc are contributed by chlorite and other components characteristic of basic
volcanic debris. The data suggest that these formations were generated by chemical and clastic
sedimentary processes on a shallow shelf. During transgression, chemical precipitation took place at the
sediment-water interface, whereas at the time of regression. Iron ore formed with sedimentary structures
and textures in Kammatturu area, in a setting where the water column was oxygenated.
Experimental Investigation on Characteristic Study of the Carbon Steel C45 in...IJMER
In this paper, the mechanical characteristics of C45 medium carbon steel are investigated
under various working conditions. The main characteristic to be studied on this paper is impact toughness
of the material with different configurations and the experiment were carried out on charpy impact testing
equipment. This study reveals the ability of the material to absorb energy up to failure for various
specimen configurations under different heat treated conditions and the corresponding results were
compared with the analysis outcome
Non linear analysis of Robot Gun Support Structure using Equivalent Dynamic A...IJMER
Robot guns are being increasingly employed in automotive manufacturing to replace
risky jobs and also to increase productivity. Using a single robot for a single operation proves to be
expensive. Hence for cost optimization, multiple guns are mounted on a single robot and multiple
operations are performed. Robot Gun structure is an efficient way in which multiple welds can be done
simultaneously. However mounting several weld guns on a single structure induces a variety of
dynamic loads, especially during movement of the robot arm as it maneuvers to reach the weld
locations. The primary idea employed in this paper, is to model those dynamic loads as equivalent G
force loads in FEA. This approach will be on the conservative side, and will be saving time and
subsequently cost efficient. The approach of the paper is towards creating a standard operating
procedure when it comes to analysis of such structures, with emphasis on deploying various technical
aspects of FEA such as Non Linear Geometry, Multipoint Constraint Contact Algorithm, Multizone
meshing .
Static Analysis of Go-Kart Chassis by Analytical and Solid Works SimulationIJMER
This paper aims to do modelling, simulation and performing the static analysis of a go
kart chassis consisting of Circular beams. Modelling, simulations and analysis are performed using 3-D
modelling software i.e. Solid Works and ANSYS according to the rulebook provided by Indian Society of
New Era Engineers (ISNEE) for National Go Kart Championship (NGKC-14).The maximum deflection is
determined by performing static analysis. Computed results are then compared to analytical calculation,
where it is found that the location of maximum deflection agrees well with theoretical approximation but
varies on magnitude aspect.
In récent year various vehicle introduced in market but due to limitation in
carbon émission and BS Séries limitd speed availability vehicle in the market and causing of
environnent pollution over few year There is need to decrease dependancy on fuel vehicle.
bicycle is to be modified for optional in the future To implement new technique using change in
pedal assembly and variable speed gearbox such as planetary gear optimise speed of vehicle
with variable speed ratio.To increase the efficiency of bicycle for confortable drive and to
reduce torque appli éd on bicycle. we introduced epicyclic gear box in which transmission done
throgh Chain Drive (i.e. Sprocket )to rear wheel with help of Epicyclical gear Box to give
number of différent Speed during driving.To reduce torque requirent in the cycle with change in
the pedal mechanism
Integration of Struts & Spring & Hibernate for Enterprise ApplicationsIJMER
The proposal of this paper is to present Spring Framework which is widely used in
developing enterprise applications. Considering the current state where applications are developed using
the EJB model, Spring Framework assert that ordinary java beans(POJO) can be utilize with minimal
modifications. This modular framework can be used to develop the application faster and can reduce
complexity. This paper will highlight the design overview of Spring Framework along with its features that
have made the framework useful. The integration of multiple frameworks for an E-commerce system has
also been addressed in this paper. This paper also proposes structure for a website based on integration of
Spring, Hibernate and Struts Framework.
Microcontroller Based Automatic Sprinkler Irrigation SystemIJMER
Microcontroller based Automatic Sprinkler System is a new concept of using
intelligence power of embedded technology in the sprinkler irrigation work. Designed system replaces
the conventional manual work involved in sprinkler irrigation to automatic process. Using this system a
farmer is protected against adverse inhuman weather conditions, tedious work of changing over of
sprinkler water pipe lines & risk of accident due to high pressure in the water pipe line. Overall
sprinkler irrigation work is transformed in to a comfortableautomatic work. This system provides
flexibility & accuracy in respect of time set for the operation of a sprinkler water pipe lines. In present
work the author has designed and developed an automatic sprinkler irrigation system which is
controlled and monitored by a microcontroller interfaced with solenoid valves.
On some locally closed sets and spaces in Ideal Topological SpacesIJMER
In this paper we introduce and characterize some new generalized locally closed sets
known as
δ
ˆ
s-locally closed sets and spaces are known as
δ
ˆ
s-normal space and
δ
ˆ
s-connected space and
discussed some of their properties
Intrusion Detection and Forensics based on decision tree and Association rule...IJMER
This paper present an approach based on the combination of, two techniques using
decision tree and Association rule mining for Probe attack detection. This approach proves to be
better than the traditional approach of generating rules for fuzzy expert system by clustering methods.
Association rule mining for selecting the best attributes together and decision tree for identifying the
best parameters together to create the rules for fuzzy expert system. After that rules for fuzzy expert
system are generated using association rule mining and decision trees. Decision trees is generated for
dataset and to find the basic parameters for creating the membership functions of fuzzy inference
system. Membership functions are generated for the probe attack. Based on these rules we have
created the fuzzy inference system that is used as an input to neuro-fuzzy system. Fuzzy inference
system is loaded to neuro-fuzzy toolbox as an input and the final ANFIS structure is generated for
outcome of neuro-fuzzy approach. The experiments and evaluations of the proposed method were
done with NSL-KDD intrusion detection dataset. As the experimental results, the proposed approach
based on the combination of, two techniques using decision tree and Association rule mining
efficiently detected probe attacks. Experimental results shows better results for detecting intrusions as
compared to others existing methods
Natural Language Ambiguity and its Effect on Machine LearningIJMER
"Natural language processing" here refers to the use and ability of systems to process
sentences in a natural language such as English, rather than in a specialized artificial computer
language such as C++. The systems of real interest here are digital computers of the type we think of as
personal computers and mainframes. Of course humans can process natural languages, but for us the
question is whether digital computers can or ever will process natural languages. We have tried to
explore in depth and break down the types of ambiguities persistent throughout the natural languages
and provide an answer to the question “How it affects the machine translation process and thereby
machine learning as whole?” .
Today in era of software industry there is no perfect software framework available for
analysis and software development. Currently there are enormous number of software development
process exists which can be implemented to stabilize the process of developing a software system. But no
perfect system is recognized till yet which can help software developers for opting of best software
development process. This paper present the framework of skillful system combined with Likert scale. With
the help of Likert scale we define a rule based model and delegate some mass score to every process and
develop one tool name as MuxSet which will help the software developers to select an appropriate
development process that may enhance the probability of system success.
Material Parameter and Effect of Thermal Load on Functionally Graded CylindersIJMER
The present study investigates the creep in a thick-walled composite cylinders made
up of aluminum/aluminum alloy matrix and reinforced with silicon carbide particles. The distribution
of SiCp is assumed to be either uniform or decreasing linearly from the inner to the outer radius of
the cylinder. The creep behavior of the cylinder has been described by threshold stress based creep
law with a stress exponent of 5. The composite cylinders are subjected to internal pressure which is
applied gradually and steady state condition of stress is assumed. The creep parameters required to
be used in creep law, are extracted by conducting regression analysis on the available experimental
results. The mathematical models have been developed to describe steady state creep in the composite
cylinder by using von-Mises criterion. Regression analysis is used to obtain the creep parameters
required in the study. The basic equilibrium equation of the cylinder and other constitutive equations
have been solved to obtain creep stresses in the cylinder. The effect of varying particle size, particle
content and temperature on the stresses in the composite cylinder has been analyzed. The study
revealed that the stress distributions in the cylinder do not vary significantly for various combinations
of particle size, particle content and operating temperature except for slight variation observed for
varying particle content. Functionally Graded Materials (FGMs) emerged and led to the development
of superior heat resistant materials.
Energy Audit is the systematic process for finding out the energy conservation
opportunities in industrial processes. The project carried out studies on various energy conservation
measures application in areas like lighting, motors, compressors, transformer, ventilation system etc.
In this investigation, studied the technical aspects of the various measures along with its cost benefit
analysis.
Investigation found that major areas of energy conservation are-
1. Energy efficient lighting schemes.
2. Use of electronic ballast instead of copper ballast.
3. Use of wind ventilators for ventilation.
4. Use of VFD for compressor.
5. Transparent roofing sheets to reduce energy consumption.
So Energy Audit is the only perfect & analyzed way of meeting the Industrial Energy Conservation.
An Implementation of I2C Slave Interface using Verilog HDLIJMER
The focus of this paper is on implementation of Inter Integrated Circuit (I2C) protocol
following slave module for no data loss. In this paper, the principle and the operation of I2C bus protocol
will be introduced. It follows the I2C specification to provide device addressing, read/write operation and
an acknowledgement. The programmable nature of device provide users with the flexibility of configuring
the I2C slave device to any legal slave address to avoid the slave address collision on an I2C bus with
multiple slave devices. This paper demonstrates how I2C Master controller transmits and receives data to
and from the Slave with proper synchronization.
The module is designed in Verilog and simulated in ModelSim. The design is also synthesized in Xilinx
XST 14.1. This module acts as a slave for the microprocessor which can be customized for no data loss.
Discrete Model of Two Predators competing for One PreyIJMER
This paper investigates the dynamical behavior of a discrete model of one prey two
predator systems. The equilibrium points and their stability are analyzed. Time series plots are obtained
for different sets of parameter values. Also bifurcation diagrams are plotted to show dynamical behavior
of the system in selected range of growth parameter
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
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A method for solving quadratic programming problems having linearly factorized objective function
1. International
OPEN ACCESS Journal
Of Modern Engineering Research (IJMER)
| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 4 | Iss.8| Aug. 2014 | 20|
A method for solving quadratic programming problems having
linearly factorized objective function
M. Jayalakshmi1, P. Pandian2
1 Department of Mathematics, School of Advanced Sciences,VIT University, Vellore-14, India.
I. Introduction
Non-linear programming problem is an optimization problem in which either the objective function is
non-linear, or one or more constraints have non-linear relationship or both. A quadratic programming (QP)
problem is the simplest non-linear programming problem in which the objective function is quadratic and the
constraints are linear. Because of its usefulness in Management Science, Health Science and Engineering, QP is
viewed as a discipline in Operational Research and it has become a fertile area in the field of research in recent
years. A large number of algorithms for solving QP problems have been developed. Some of them are
extensions of the simplex method and others are based on different principles. In the literature, a great number
of methods (Wolfe [1], Beale [2], Frank and Wolfe [3], Shetty [4], Lemke [5], Best and Ritter [6], Theil and
van de Panne [7], Boot [8], Fletcher [9], Swarup[10], Gupta and Sharma[11], Moraru [12,13], Jensen and
King[14], Bazaraa et al.[15]) are available to solve QP problems. Among them, Wolf’s method [1], Swarup’s
simplex method [10] and Gupta and Sharma’s method [11] are more popular than the other methods.
Quazzafi Rabbani and Yusuf Adhami [16] used modified Fourier elimination method for solving QP
problems after applying the K-T conditions. Babul Hasan [17] has developed a computer oriented solution
method for solving special type of QP problems in which the objective function is a quasi-concave in the
feasible region and it can be factorized into two linear functions such that both linear factors are positive in the
feasible region. Jan Busa [18] proposed a regularization method for solving the QP problem with linear
constraints containing absolute values of variables.
In this paper, we propose a new method namely, objective separable method for finding an optimal
solution to a QP problem in which the objective function can be factorized into two linear functions. In this
proposed method, we construct two linear programming problems both of maximization type from the given QP
problem and then, we obtain an optimal solution to the given QP problem from the solutions of the two
constructed linear programming problems. The objective separable method is based only on the simplex method
which differs from the existing methods (Wolfe’s method [1], Beale’s algorithm [2], Swarup’s simplex method
[10] and Babul Hasan method [17]). Numerical example is given for better understanding the solution procedure
of the proposed method.
II. Preliminaries
We need the following definition and the result which can be found in Ezio Marchi [19].
DEFINITION 2.1. Let f1(x) and f2(x) be two differentiable functions defined on
n X R , an n-dimensional
Euclidean space. The functions f1(x) and f2(x) are said to have the Gonzi property in
n X R if ( f1(x) f1(u))( f2(x) f2(u)) 0, for all x,u X .
THEOREM 2.1 The product f1(x) f2(x) of two linear functions f1(x) and f2(x) is concave if and only
if the functions f1(x) and f2(x) have the Gonzi property.
Abstract: A new method namely, objective separable method based on simplex method is proposed for
finding an optimal solution to a quadratic programming problem in which the objective function can be
factorized into two linear functions. The solution procedure of the proposed method is illustrated with the
numerical example.
Keywords: Quadratic programming problem, Linear programming problem, Objective separable
method.
2. A method for solving quadratic programming problems having linearly factorized objective function
| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 4 | Iss.8| Aug. 2014 | 21|
III. Quadratic Programming Problems
Consider the following general form of a QP problem:
Maximize f (X)
subject to AX B, X 0
where f R R n : is a quadratic function on
n R , X is an n-dimensional column vector X, A is an (m n)
matrix and B is an m-dimensional column vector.
In this paper, we consider a special type of QP problem in which the objective function can be factorized
into two linear functions. Such QP problem can be represented as follows:
(P) Maximize Z X C X D X T T ( )
subject to AX B, X 0
where A is an (m n) matrix, B is an m-dimensional column vector, X, C, D are n-dimensional column vectors
and , are real numbers.
Now, we assume that the two functions C X T
and D X T
have the Gonzi property in the
feasible set and the set of all feasible solutions to the problem (P) are non-empty and bounded. Thus, by the
Theorem 2.1., it is concluded that the problem (P) is a concave non-linear programming problem with linear
constraints. This implies that the optimal solution of the problem (P) exists and it occurs at an extreme point of
the feasible region.
Now, from the problem (P), two single objective linear programming problems are constructed as follows:
P1 Maximize Z X C X T 1( )
subject to AX b , X 0
and
P2 Maximize Z X D X T 2( )
subject to AX b , X 0 .
REMARK 3.1: From the above theorem, we can easily conclude that if both P1 and P2 are solvable, then
(P) is solvable.
Now, we prove the following theorem connecting the optimal solutions of the problem (P), the problem
P1 and the problem P2 which is used in the proposed method.
THEOREM 3.1: Let X0 be an optimal solution to the problem P1 . If {Xn } is a sequence of basic
feasible solutions to the problem P2 by simplex method considering the solution X0 as an initial feasible
solution such that Z(Xk ) Z(Xk1) for all k 0,1,2,...,n and either Xn1 is an optimal solution to the
problem P2 or Z(Xn1) Z(Xn2) , then Xn1 is an optimal solution to the problem (P).
PROOF: It is obvious that Xn1 is a feasible solution to the problem (P)
Let V be a feasible solution to the problem (P).
Now, since Xn1 is an optimal solution to the problemP2 , we have
Z2(V) Z2(Xn1) .
Case(i): Now, since Z(Xk ) Z(Xk1) , for all k 0,1,2,...,n and Xn1 is an optimal solution to the
problemP2 , we can conclude that Z(Xn1) Z(V) . Therefore, Xn1 is an optimal solution to the
problem (P).
Case(ii): Now, since Z(Xk ) Z(Xk1) for all k 0,1,2,...,n and Z(Xn1) Z(Xn2) , we can
conclude that Z(Xn1) Z(V) . Therefore, Xn1 is an optimal solution to the problem (P).
Hence the theorem is proved.
3. A method for solving quadratic programming problems having linearly factorized objective function
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IV. Objective Separable Method
Now, we proposed a new method namely, objective separable method for finding an optimal solution to the QP
problem.
The proposed method proceeds as follows:
Step 1: Construct two single objective linear programming problems namely, the problem P1 and the
problem P2 from the given problem (P).
Step 2: Compute the optimal solution to the problem P1 using the simplex method. Let the optimal solution
to the problem P1 be X and the maximum value of Z1(X) Z1(X) .
Step 3: Use the optimal table of the problem P1 as an initial simplex table for the problemP2 , and obtain a
sequence of basic feasible solutions to the problem P2 by the simplex method.
Step 4: Let {Xn } be a sequence of basic feasible solutions to the problem P2 obtained by the Step 3. If
Z(Xk ) Z(Xk1) for all k 0,1,2,...,n and Xn1 is an optimal solution to the problem P2 for some n,
stop the computation process and then, go to the Step 5 or Step 6.
Step 5: If Z(Xk ) Z(Xk1) for all k 0,1,2,...,n and Z(Xn1) Z(Xn2) , then stop the computation
process and then, go to the Step 6.
Step 6: Xn1 is an optimal solution to the problem (P) and the maximum value of ( ) ( ) 1 n Z X Z X by the
Theorem 3.1.
REMARK 4.1: The maximum value for (n +1) is less than or equal to the number of the iterations to obtain the
optimal solution to the problem P2 by the simplex method.
The proposed method for solving the QP problem is illustrated by the following examples.
EXAMPLE 4.1: Consider the following QP problem.
(P) Maximize 2 4 1 2 2 1 2 3 1 2 3 Z x x x x x x
subject to 3 4 1 2 x x ; 2 3 1 2 x x ; 4 3 2 3 x x ; , , 0 1 2 3 x x x .
The following two LP problems can be obtained from the given problem:
P1 Maximize Z1(X) 2x1 4x2 x3 1
subject to 3 4 1 2 x x ; 2 3 1 2 x x ; 4 3 2 3 x x ; , , 0 1 2 3 x x x .
and
P2 Maximize Z2(X) x1 x2 2x3 2
subject to 3 4 1 2 x x ; 2 3 1 2 x x ; 4 3 2 3 x x ; , , 0 1 2 3 x x x .
Now, by simplex method, the optimal solution to the problem P1 is 1 1 x , 1 2 x ,
2
1
3 x , Max.
2
15
Z1 and the value of
2
45
Z .
Now, by the Step 3 of the proposed method, the solution to the problem P2 by simplex method is given
below:
4. A method for solving quadratic programming problems having linearly factorized objective function
| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 4 | Iss.8| Aug. 2014 | 23|
Iteration Solution
(x1, x2, x3, s1, s2, s3)
Value of Z1 Value of Z2 Value of
Z Z1Z2
0 X0 = ,0,0,0)
2
1
(1,1,
2
15
3
2
45
1
X1 = ,0,0)
2
5
,
4
3
,0,
2
3
(
4
19
5
4
95
Since the 1st iteration table is optimal and by the Step 4 of the proposed method, the optimal solution to the
given quadratic programming problem is
2
3
1 x , 0 2 x ,
4
3
3 x and Maximum value of
4
95
Z .
EXAMPLE 4.2: Consider the following QP problem.
(P) Maximize Z (x1 x2 4)(x1 x2 2)
subject to 2 2 1 2 x x ; 4 1 2 x x ; , 0 1 2 x x .
The following two LP problems can be obtained from the given problem:
P1 Maximize Z1 x1 x2 4
subject to 2 2 1 2 x x ; 4 1 2 x x ; , 0 1 2 x x .
and
P2 Maximize Z2 x1 x2 2
subject to 2 2 1 2 x x ; 4 1 2 x x ; , 0 1 2 x x .
Now, by simplex method, the optimal solution to the problem P1 is x1 0 , x2 1, Max. Z1 5 and the
value of Z 5 .
Now, by the Step 3 of the proposed method, the solution to the problem P2 by simplex method is given
below:
Iteration Solution
( , , , ) 1 2 1 2 x x s s
Value of Z1 Value of Z2 Value of
Z Z1Z2
0
X0 = (0,1,0,3) 5 1 5
1
X1 = (2,2,0,0) 4 2 8
2
X2 = (4,0,6,0) 0 6 0
Since the 2nd iteration table is optimal and by the Step 4 of the proposed method, the optimal solution to the
given linear quadratic programming problem is x1 0 , 0 2 x and the Maximum value of Z 8.
V. Conclusion
The objective separable method is proposed to solve QP problems in which the objective function can
be factorized into two linear functions. Since the proposed method is based on simplex method, without using
KKT conditions and complementarity constraints [2]. Also, we can solve such QP problems using the existing
LP solvers. Further, the present work can be extended to integer QP problems and fully fuzzy QP problems.
REFERENCES
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[2] E.M.L. Beale, On quadratic programming, Naval Research Logistics Quarterly, 6, 1959, 227-243.
[3] M. Frank, P. Wolfe, An algorithm for quadratic programming, Naval Research Logistics Quarterly, 3, 1956, 95–110.
[4] C.M. Shetty, A simplified procedure for quadratic programming, Operations Research, 11, 1963, 248–260.
[5] C.E. Lemke, Bi-matrix equilibrium points and mathematical programming, Management Science 11, 1965, 681–689.
[6] M.J. Best, K. Ritter K, A quadratic programming algorithm, Zeitschrift for Operations Research, 32, 1988, 271–297.
[7] H. Theil, C. Van de Panne, 1961. Quadratic programming as an extension of conventional quadratic maximization,
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| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 4 | Iss.8| Aug. 2014 | 24|
[8] J.C.G., Boot, Notes on quadratic programming: The Kuhn-Tucker and Theil-van de Panne conditions, degeneracy and equality constraints, Management Science, 8, 1961, 85–98. [9] R. Fletcher, A general quadratic programming algorithm, J. Inst., Maths. Applics 7, 1971, 76–91. [10] K. Swarup, Quadratic Programming, CCERO (Belgium) 8, 1966, 132-136. [11]. A.K. Gupta, J.K. Sharma, A generalized simplex technique for solving quadratic programming problem, Indian Journal of Technology, 21, 1983, 198-201. [12] V. Moraru, An algorithm for solving quadratic programming problems, Computer Science Journal of Moldova 5, 1997, 223-235. [13] V. Moraru, Primal-dual method for solving convex quadratic programming problems, Computer Science Journal of Moldova, 8, 2000, 209-220. [14] D.L. Jensen, A.J. King, A decomposition method for quadratic programming, IBM Systems Journal 31, 1992, 39– 48. [15] M. Bazaraa, H. Sherali, C.M. Shetty, Nonlinear programming: Theory and Algorithms (John Wiley, New York, 2006). [16] Quazzafi Rabbani, A. Yusuf Adhami, Modified Fourier’s method for solving quadratic programming problems, International Journal of Mathematical Archive, 2, 2011, 2005-2012. [17] M. Babul Hasan, A technique for solving special type quadratic programming problems, Dhaka University Journal of Sciences, 60, 2012, 209-215. [18] Jan Busa, Solving quadratic programming problem with linear constraints containing absolute values, Acta Electrotechnica et Informatica, 12, 2012, 11–18. [19] Ezio Marchi, When is the product of two concave functions concave?, IMA Preprint Series # 2204, Institute for Mathematics and its Applications, University of Minnesota, 2008, 1-8.