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

Related Topics

• Solver-Based Optimization Problem Setup