The document discusses different types of optimization techniques including nonlinear optimization, unconstrained optimization, and equality constrained optimization. Nonlinear optimization involves using Taylor series expansions to minimize the residue between a data fit curve and actual data points. Unconstrained optimization seeks to minimize a function subject to variables being greater than or equal to 0. Equality constrained optimization uses Lagrange equations to minimize a function subject to an equality constraint, where the Lagrange multiplier determines if the solution is a minimum or maximum.

1. Optimization
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Presented by: vikas sinha

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3. #1 Non-linear optimization
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residue
fit
Data
Let us consider,
Taylor series expansion :
…(1)
…(2)
…(3)

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{D} =[Zj]*{∆A}+[E]
∆a
∆b
…(4)
…(5)
…(6)
Cont…

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Cont…
…(7)

6. Cont…
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t Yi Yfit Ynewfit
10 3.1 1.95 ?
40 11.9 7.25 ?
80 21 13.2 ?
140 29.9 20.1 ?
200 37.3 25.3 ?
300 42.7 31.08 ?
let

7. z=
D=
.0477 380.49
.1812 1309.96
.33 2145.02
.503 2780.87
.633 2943.035
.777 2677.56
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3.1-1.95
11.9-7.25
21-13.2
29.9-20.1
37.3-25.3
42.7-31.08
Cont…

8. ∆a=5.02, ∆b=.0002
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…(8)
Cont…
In this way,
…(9)
…(10)

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#2 Unconstraint optimization:
To minimize y=f(xi)
X1,x2,x3>=0
…(11)
…(12)
…(13)

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Constrained optimization
Constrained
optimization
equality inequality

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#3 Equality Constrained
To minimize y=f(x1,x2)
If it is subjected to g(x1,x2)=0
lagrange equation:
L=f(x1,x2)+λg(x1,x2)
…(14)
…(12)
…(15)>0; minimum
= <0; maximum

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