MATLAB Optimization Techniques by César Pérez López

Author:César Pérez López
Language: eng
Format: epub
Publisher: Apress, Berkeley, CA

>> [x,fval] = fminsearch(inline('100*(x(2)-x(1)^2)^2+...

1-x (1)) ^ 2'), [- 1.2, 1])

x =

1.0000 1.0000

FVal =

8. 1777e-010

The following example computes a zero of the sine function near 3 and a zero of the cosine function between 1 and 2.

>> x = fzero(@sin,3)

x =

3.1416

>> x = fzero(@cos,[1 2])

x =

1.5708

7.6 Conditional Minima and Maxima. The Method of “Lagrange Multipliers”

Suppose we want to optimize (i.e. maximize or minimize) the function f(x1,x2,…,xn) , called the objective function, but subject to certain restrictions given by the equations:

g 1 (x 1 ,x 2 ,…,x n )=0

g 2 (x 1 ,x 2 ,…,x n )=0

...............

g k (x 1 ,x 2 ,…,x n )=0

This is the setting in which the Lagrangian is introduced. The Lagrangian is a linear combination of the objective function and the constraints, and has the following form:

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