Question

Give me a working MATLAB code for the Golden section search method . It should be working

Dont answer if you do not know,

the code must work for the golden section method

Answer 1

clc; clear all; clc;

phi = double( (sqrt(5)-1) / 2 ); % golden ratio
del = .05;% small increment value
epsilon = .001; % function difference precision

max_iter = 100; % maximum number of iterations for Phase I and II.

alpha(1) = 0; % first value of alpha
alpha(2) = del; % second value of alpha is equal to the small increment value

% begin iterations for Phase I
i_iter = 1;
while i_iter <= max_iter
  
if ( f(alpha(i_iter)) > f(alpha(i_iter + 1)) )
alpha(i_iter + 2) = 0;

for j_iter = 1 : i_iter+1
alpha(i_iter + 2) = alpha(i_iter + 2) + del*(1.618)^(j_iter-1);
end
else
break
end
  
i_iter = i_iter + 1; % increment number of iterations by 1
end

% the uncertainity interval
alpha_l = 0; % set lower bound of alpha since it cannot be known how many alphas will be enough, i.e. alpha(i_iter - 2) may be null.
alpha_u = alpha(i_iter + 1);

% plot the line search function of one variable (i.e., alpha - a)
figure; hold on;
syms a;
fplot(@f,[alpha_l alpha_u],'b');
% plot title and axes labels
title( 'Golden section search on f ( alpha )' );
xlabel('alpha');
ylabel('f (alpha)');

% divide uncertainity interval using golden ratio, (i.e., set new interval
% boundaries)
a = alpha_l + (1 - phi)*(alpha_u - alpha_l);  
b = alpha_l + phi*(alpha_u - alpha_l);

% calculate function values at points
f_a = f(a);
f_b = f(b);

% plot new interval boundaries on top of the function plot.
plot(a,f_a,'rd')
plot(b,f_b,'rd')

% begin iterations for Phase II
i_iter = 1;
while ( ( abs(alpha_u-alpha_l) > epsilon ) && (i_iter < max_iter) ) && (i_iter < max_iter)
if(f_a < f_b)
alpha_u = b;
b = a;
a = alpha_l + (1 - phi)*(alpha_u - alpha_l);
  
f_a=f(a);
f_b=f(b);
  
plot(a,f_a,'rd');
else
alpha_l = a;
a = b;
b = alpha_l + phi*(alpha_u - alpha_l);
  
f_a = f(a);
f_b = f(b);
  
plot(b, f_b, 'rd')
end
end

% print alpha value that minimizes the line search function
if(f_a<f_b)
fprintf('\nalpha_min = %f\n', a)
fprintf('f_min = %f\n', f_a)
plot(a,f_a,'kd', 'LineWidth', 1, 'MarkerSize', 10, 'MarkerFaceColor' , 'g')
  
else
fprintf('\nalpha_min = %f\n', b)
fprintf('f_min = %f\n', f_b)
plot(b,f_b,'kd', 'LineWidth', 1, 'MarkerSize', 10, 'MarkerFaceColor' , 'g')
end