Converting Non-linear Programming Problem from Maximization to Minimization

Question

I have a non-linear maximization problem and I want to convert it to be a minimization problem, can I do so by multiplying it by a negative sign, or is that wrong; and if that is wrong what should I do?

Thanks a lot

Since I answered your question.... would you consider selecting it as the answer by selecting the check mark. And welcome to SE Mathematics! — Squirtle, Jan 24 '14 at 18:15

score 3 · Answer 1 · answered Jan 18 '14 at 22:10

3

Yes $$f:X \to \mathbb{F}$$

$$\max_{x \in X} f(x) = -\min_{x \in X} f(x)$$

Consider for example, the non-linear maximization problem

$$\max_{x \in \mathbb{R}} -x^2 $$

this is equivalent to minimizing $x^2($in the sense that the minimizer for this is $x=0$ and your original function is maximized when $x=0)$

answered Jan 18 '14 at 22:10

Squirtle

6,698

2

In fact, that it is nonlinear has nothing to do with this answer. – Squirtle Jan 18 '14 at 22:11

Converting Non-linear Programming Problem from Maximization to Minimization

1 Answers1