Page 327 - MATLAB an introduction with applications

312 ——— MATLAB: An Introduction with Applications

X=X+s*V;
% IDENTIFY BIGGEST DECREASE OF F
% AND UPDATE SEARCH DIRECTIONS
imax=1; dfmax=df(1);
for i=2:N
if df(i)>dfmax imax=i; dfmax=df(i); end
end
for i=imax:N–1
u(1:N,i)=u(1:N,i+1);
end
u(1:N,N)=V;
end
fprintf(‘Optimum point after %d cycles is\n’,n);
fprintf(‘%f\n%f\n’,X(1),X(2));

Function is
function z=fline(s)
global X V
b1=V(1);
b2=V(2);
a1=X(1);a2=X(2);
p1=a1+s*b1;p2=a2+s*b2;
z=4*p1^2+3*p2^2–5*p1*p2–8*p1;
Optimum point after 30 cycles is
2.091345
1.739733
Actual output from MATLAB function fminsearch(‘fxy’, [0 0]) is
2.0870
1.7392

2
2
Example E5.29: Find the minimum value of the function f(X) = 7x + 5x –8x x –5x starting from (0, 0)
1
1 2
1
2
using Powell’s method.
Solution: The following program is used
global X V
X=[0;0]; %STARTING POINT
N=length(X);% number of design variables
df=zeros(N,1);% decreases of f stored here
u=eye(N); % columns of u store search directions V
n=30; % Number of cycles
for j=1:n
xold=X;