How to find maximum of a multivariable function using max()

How to find maximum of a multivariable function using max(). Let's denote z = (y+cos(y))/(x^2) for x,y belonging to [1,15].

[darova]

try

max(z(:))

Answer 1

[Ameer Hamza]

You can use fmincon function to find maximum value

z = @(x,y) (y+cos(y))./(x.^2);

sol = fmincon(@(x) -z(x(1),x(2)), 10*rand(2,1), [], [], [], [], [1;1], [15;15]);
x_sol = sol(1);
y_sol = sol(2);

[madhan ravi]

I think you mean't

y_sol = sol(2)

[Ameer Hamza]

madhan, Thanks for pointing out.

[enter]

If I use fmincon a few times it tends to give bad results

[Ameer Hamza]

Michal, this is the limitation of the numerical optimization algorithm. They are sensitive to the initial guess. I found that for your objective function, 'interior-point' algorithm gives consistent results.

z = @(x,y) (y+cos(y))./(x.^2);
opts = optimoptions('fmincon', 'Algorithm', 'interior-point');
sol = fmincon(@(x) -z(x(1),x(2)), rand(1,2), [], [], [], [], [1;1], [15;15], [], opts);
x_sol = sol(1);
y_sol = sol(2);