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Maximizing vs. Minimizing

Global Optimization Toolbox optimization functions minimize the objective (or fitness) function. That is, they solve problems of the form


If you want to maximize f(x), minimize –f(x), because the point at which the minimum of –f(x) occurs is the same as the point at which the maximum of f(x) occurs.

For example, suppose you want to maximize the function


Write a function to compute


and then minimize g(x). Start from the point x0 = [0 0].

f = @(x)exp(-(x(1)^2 + x(2)^2))*(x(1)^2 - 2*x(1)*x(2) + 6*x(1) + 4*x(2)^2 - 3*x(2));
g = @(x)-f(x);
x0 = [0 0];
[xmin,gmin] = fminsearch(g,x0)
xmin =

    0.5550   -0.5919

gmin =


The maximum of f is the value of f(xmin), which is –gmin.

ans =


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