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I have a simple doubt, we know that $$\min f(x)=-\max(-f(x)),$$ but suppose we have an optimization problem, say a linear programming problem, such that the objective is to minimize $f(x)$. If we want to write it as a maximization problem, we write it as $\max(-f(x))$. My doubt is, why it will not be $-\max(-f(x))$.

This may be a very silly question, my apologies, but I have always wondered why is it so.

Ottavio
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Cherryblossoms
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1 Answers1

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Not a silly question. It is not possible to write $- \max (-f(x))$ in advance as the value of the maximum is simply not known.

So what we do is, we first calculate $\max (-f(x))$ and then multiply by $-1$.

Hyperbolic PDE friend
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