Golden section search algorithm

Errors :

with the same size and shape as the input arguments.

> In matlab.graphics.function.FunctionLine>getFunction

In matlab.graphics.function/FunctionLine/updateFunction

In matlab.graphics.function.FunctionLine.set.Function_I

In matlab.graphics.function.FunctionLine.set.Function

In matlab.graphics.function.FunctionLine

In fplot>singleFplot (line 245)

In fplot>@(f)singleFplot(cax,{f},limits,extraOpts,args) (line 200)

In fplot>vectorizeFplot (line 200)

In fplot (line 166)

In goldensection (line 30)

Matlab code :

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

hold off;

saveas(gcf,'results_plot.png')

function y = f(a)

% This function returns the value of the line search function for a given

% value of function variable.

% y = 2 - 4*a + exp(a); % Example 10.3 in the book (Arora)

% y = (11*a - 5)^2 + 16*a^2; % Homework 3 / Section B - a

% y = 0.1*(5 - a)^2 + (1 - 2*a)^2; % Homework 3 / Section B - b

y =(-19+2358*a)^2+5*(-1+588*a)^2+(-4+880*a)^4+10*(-3+2208*a)^4;

end

Answer 1

[Pratyush Roy]

Hi,

fplot prefers to pass a vector to the function for efficiency, but checks whether that works and gives a warning if it doesn't work. As a workaround, you can consider changing the function f in a manner as follows:

function y = f(a)

%Here we assume that a is an array and the function works on every element of a 
%to return a corresponding element in the y array.

for i=1:numel(a)
    y(i) =(-19+2358.*a(i)).^2 + 5*(-1+588.*a(i)).^2 + (-4+880.*a(i)).^4 + 10.*(-3+2208.*a(i)).^4; 
end
end

Hope this helps!