How to write this constraint in an optimization problem?

Asked Nov 24 '15 at 16:43

Active Nov 24 '15 at 16:43

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Let $x_i$ be a binary variable in the set $\{0,1\}$ for all $i$ in the set $\{1,\ldots,n\}$, i.e., $x_i\in\{0,1\},\,\forall\,i\in\{0,\ldots,n\}$.

I would like to write the constraint:

$$\displaystyle\prod_{\substack{i=1\\ x_i\neq0}}^nA_ix_i>A,$$ where $A_i$ and $A$ are given as inputs.

asked Nov 24 '15 at 16:43

drzbir

What do you mean you want to write the constraint? you already have. – Kuifje Nov 24 '15 at 21:35
I mean how to write it in a solver for example. The subscript $x_i\neq0$ makes it difficult for me to write it. – drzbir Nov 24 '15 at 21:42
There are different issues: first the constraint is not linear, second constraints with $<$ or $>$ signs are never used in optimization. The $x_i\neq 0$ should not be a problem. What solver are you using? – Kuifje Nov 24 '15 at 21:44
I would like to use cplex solver. – drzbir Nov 24 '15 at 21:44
do you need a linear form for your model? – Kuifje Nov 24 '15 at 21:46
you can write $x_i \neq 0$ with an if condition, something like: for all $i$ in $1,…,n$, if $x_i \neq 0$... – Kuifje Nov 24 '15 at 21:47
Thanks. I thought about applying the log function. – drzbir Nov 24 '15 at 21:49
Yes that is an idea to transform a product into a sum, although it will remain non linear. – Kuifje Nov 24 '15 at 21:50
Do you know how to linearize that product? – drzbir Nov 25 '15 at 23:08

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