Introduction to Optimization - Numerical Methods in Engineering with MATLAB - page 402

h T 2 0 T , we arrive at the following

Letting x = θ and starting with x 0 =

program:

% Example 10.6 (Minimization with Fletcher-Reeves)
global X FUNC DFUNC
FUNC = @fex10 _ _ 6; DFUNC = @dfex10 6;

X = [2.0;0.0];
[xMin,fMin,nCyc] = fletcherReeves;
b = 8.0/X(1) - X(1)*tan(X(2));
theta = X(2)*180.0/pi; % Convert into degrees
fprintf('b = %8.5f\n',b)
fprintf('h = %8.5f\n',X(1))
fprintf('theta = %8.5f\n',theta)
fprintf('perimeter = %8.5f\n',fMin)
fprintf('number of cycles = %2.0f',nCyc)

Note that the starting point X and the function handles FUNC (functiondefining
F ) and DFUNC (functiondefining

∇ F ) are declared global . The M-files for the two

functions are

_ functiony=fex10 6(X)

% Function defining F in Example 10.6
y = 8.0/X(1) - X(1)*(tan(X(2)) - 2.0/cos(X(2)));

functiong=dfex10 6(X)

% Function defining grad(F) in Example 10.6
g = zeros(2,1);
g(1) = -8.0/(X(1)ˆ2) - tan(X(2)) + 2.0/cos(X(2));
g(2) = X(1)*(-1.0/cos(X(2)) + 2.0*tan(X(2)))/cos(X(2));

_

The results are( θ is in degrees):

>> b = 2.48161
h = 2.14914
theta = 30.00000
perimeter = 7.44484
number of cycles = 5