● Finding Maximum and Minimum by Golden-Section Search using MATLAB

This program implements the golden-section search algorithm. It locates the minimum or maximum of the function depending on the user’s preference, iterates until the relative error falls below a stooping criteria or exceeds an maximum number of iterations, return both the optimal x and f(x), minimizes the number of function evaluations.

r=(sqrt(5)-1)/2; %Golden Rate

disp('Number of max iteration')

maxiter=input('maxiter= ');

disp('Value of tolerance')

tol=input('Tol= ');

disp('For max enter "1", for min enter "0"')

x=input('minmax= ');

a=input('Lower bound= '); %Lower limit

b=input('Upper bound= '); %Upper limit

disp(' ')

disp('k x1 x2')

for k=1:maxiter

if (x==1) %Part that will find max

x1=a+r*(b-a); %First one of the points inside

x2=b-r*(b-a); %Second one of the points inside

fx1=-x1^4-2*x1^3-8*x1^2-5*x1; %Value of fx at first inside point

fx2=-x2^4-2*x2^3-8*x2^2-5*x2; %Value of fx at second inside point

if fx1>fx2 %Changing interval as [x2,b]

a=x2;

x2=x1;

x1=a+r*(b-a);

else

b=x1; %Changing interval as [a,x1]

x1=x2;

x2=b-r*(b-a);

end

fprintf ('%d %7.5f %7.5f\n', k,x1,x2)

%Stop if the error is below tolerance

if(abs((x1-x2))

end

else %Part that will find min

x1=a+r*(b-a);

x2=b-r*(b-a);

fx1=3+6*x1+5*x1^2+3*x1^3+4*x1^4;

fx2=3+6*x2+5*x2^2+3*x2^3+4*x2^4;

if fx1

a=x2; %Changing interval as [x2,b]

x2=x1;

x1=a+r*(b-a);

else

b=x1; %Changing interval as [a,x1]

x1=x2;

x2=b-r*(b-a);

end

fprintf ('%d %7.5f %7.5f\n', k,x1,x2)

if(abs((x1-x2))

end

end

end

disp(' ')

disp('Results')

disp('x1 x2 f(x1) f(x2)')

fprintf ('%7.5f %7.5f %7.5f %7.5f\n',x1,x2,fx1,fx2)