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August 8th, 2019, 07:57 AM   #1
Joined: Sep 2013

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How can you optimize when the constraint is a condition?


I want to minimize $-x_1*x_2*...*x_n$
The constraint is $c=0$. $c$'s value depends on the current $(x_1,...,x_n)$
If $c$ is not $0$, then $(x_1,...,x_n)$ is not a valid solution.
I have the formula to calculate $c$.
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August 8th, 2019, 12:25 PM   #2
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Depending on the form of c, one way is to rewrite the problem as an unconstrained function of (n-1) variables.

For example, to maximize $\displaystyle f(x_1,x_2,x_3) = x_1x_2x_3$ with the constraint $\displaystyle c=x_1+x_2+x_3=0$, you could rewrite this as maximizing $\displaystyle f(x_1,x_2) = x_1x_2(-x_1-x_2)$. Then just use your favourite optimization technique from there.

If c is not a "nice" function, though, then you may have to (re-)calculate $\displaystyle x_n$ and/or derivatives within optimization steps, or go to even more creative solutions.
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