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Maximizing an Objective

All solvers attempt to minimize an objective function. If you have a maximization problem, that is, a problem of the form

maxxf(x),

then define g(x) = –f(x), and minimize g.

For example, to find the maximum of tan(cos(x)) near x = 5, evaluate:

[x fval] = fminunc(@(x)-tan(cos(x)),5)
Local minimum found.

Optimization completed because the size of the gradient is less than
the default value of the function tolerance.

x =
    6.2832

fval =
   -1.5574
The maximum is 1.5574 (the negative of the reported fval), and occurs at x = 6.2832. This answer is correct since, to five digits, the maximum is tan(1) = 1.5574, which occurs at x = 2π = 6.2832.