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

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enter 2020-3-29

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评论： Ameer Hamza 2020-3-30

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].

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darova 2020-3-29

在 MATLAB Online 中打开

try

max(z(:))

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Ameer Hamza 2020-3-29

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编辑：Ameer Hamza 2020-3-30

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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);

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enter 2020-3-30

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

Ameer Hamza 2020-3-30

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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);