Page 330 - MATLAB an introduction with applications

Optimization ——— 315

Example E5.31: Repeat problem E5.31 using Fletcher-Reeves method.
Solution:
2
2
Given f (x , x ) = 7x + 5x – 8x x – 5x 1
1
1 2
2
2
1
Here gradient df = [14x – 8x – 5; 10x – 8x ] T
2
1
2
1
Complete program is as follows:
global X V
X=[0;0];
N=length(X);
g0=–feval(‘df’,X);
V=g0;
n=50;
for i=1:n
[s fmin]=fminbnd(‘fline’,–10,10);
X=X+s*V
g1=–feval(‘df’,X);
gamma=(norm(g1)/norm(g0))^2;
V=g1+gamma*V;
g0=g1;
end
fprintf(‘Minimum point for this function is \n’);
fprintf(‘%f\n%f\n’,X(1),X(2));

Functions are
function z=fline(s)
global V X
p1=X(1)+s*V(1);
p2=X(2)+s*V(2);
z=7*p1^2+5*p2^2–8*p1*p2–5*p1;
%GRADIENT FUNCTION
function y=df(X)
y=[14*X(1)–8*X(2)–5; 10*X(2)–8*X(1)];

The output is as follows:
Minimum point for this function is
0.657895
0.526316
T
The actual output from MATLAB function is [0.6579 0.5263] .