# Converting a nonlinear constraint into a linear one.

 0 I have posted the following on MO, but couldn't get any answer. So now posting it here for any help that I can get. I guess this forum doesn't support LATEX, so I am posting my question as an image. The image of the question Thanks. asked 25 Aug '15, 09:21 UbaAbd 15●1●1●6 accept rate: 0% LaTeX is indeed supported: see https://www.or-exchange.org/questions/9930/what-format-could-i-post-equations-in-or-exchange. (25 Aug '15, 15:25) Paul Rubin ♦♦

 1 Assuming that the $$z_{ijp}$$ are continuous variables, you cannot get precisely what you want. What is attainable is $c_{ip}=\begin{cases} 0 & \textrm{if }\sum_{j=1}^{s_{max}}z_{ijp}=0\\ 1 & \textrm{if }\sum_{j=1}^{s_{max}}z_{ijp}\ge\epsilon \end{cases}$for some small $$\epsilon \gt 0$$. This is a variation on a commonly asked question; try searching the forum to find an answer. answered 25 Aug '15, 15:29 Paul Rubin ♦♦ 14.6k●5●13 accept rate: 19% The matrix Z is binary valued, i.e., all the elements of Z matrix are either zero or one. (25 Aug '15, 15:37) UbaAbd In that case, it's fairly trivial: $$c_{ip}\ge z_{ijp}\,\forall j$$ and $$c_{ip}\le \sum_j z_{ijp}$$. (25 Aug '15, 15:42) Paul Rubin ♦♦ Thats perfect. Thanks @paul. (26 Aug '15, 05:02) UbaAbd
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