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August 8th, 2019, 07:57 AM  #1 
Member Joined: Sep 2013 Posts: 91 Thanks: 2  How can you optimize when the constraint is a condition?
Hello 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 $c$. 
August 8th, 2019, 12:25 PM  #2 
Senior Member Joined: Jun 2019 From: USA Posts: 120 Thanks: 40 
Depending on the form of c, one way is to rewrite the problem as an unconstrained function of (n1) 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 $\displaystyle f(x_1,x_2) = x_1x_2(x_1x_2)$. 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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condition, constraint, optimize 
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