Introduction to Optimization - Numerical Methods in Engineering with MATLAB - page 396

− ,

with Powell's method starting at the point( 1). Thisfunction has an interesting

topology. The minimum valueof F occurs at the point(1

1

1).As seeninthe figure,
there is a hump between the starting andminimumpoints which the algorithmmust
negotiate.

,

1000
800
600
400
200
0

1.5

1

0.5

1.5

1

0
-0.5

0.5

y

0

-0.5

-1

x

-1

-1.5

Solution The program that solves this unconstrained optimizationproblemis

% Example 10.3 (Powell's method of minimization)
global X FUNC
FUNC = @fex10 _ 3;

X=[-1.0;1.0];
[xMin,fMin,numCycles] = powell

Note that powell receives X and the function handle FUNC as global variables.
The routinefor the function to be minimizedis

functiony=fex10 3(X)

y = 100.0*(X(2) - X(1)ˆ2)ˆ2 + (1.0 -X(1))ˆ2;

_

Here are the results:

>> xMin =
1.0000
1.0000
fMin =
1.0072e-024
numCycles =
12