Maximizing an Objective

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

$$\underset{x}{\max }f(x)$$,

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)谭(cos (x)), 5)

Local minimum found. Optimization completed because the size of the gradient is less than the value of the optimality tolerance.

x = 6.2832

fval = -1.5574

The maximum is1.5574(the negative of the reportedfval), and occurs atx = 6.2832. This answer is correct because, to five digits, the maximum is $$\tan (1)=1.5574$$, which occurs at $$x=2\pi =6.2832$$.