Optimization

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Presented by: vikas sinha

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#1 Non-linear optimization

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residuefitData

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)

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

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…

∆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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