# Tag Info

## New answers tagged logical-constraints

2

I think this can be approached using a constraint generation technique (variant of Benders decomposition), although I have no idea if it would efficient. By reordering the rows of $A$, we can assume that $$b(z)=\left[\begin{array}{c} \hat{b}\\ c+e-z \end{array}\right]$$where $\hat{b}\in\mathbb{R}^{d-m}$, $c\in \mathbb{R}^m$, $e=(1,\dots,1)^\prime \in \mathbb{... 4 By Farkas lemma, infeasibility of$Ax\leq b$is equivalent to feasibility of$A^Ty = 0, y^Tb < 0, y\geq 0$, or more practically useful$A^Ty=0, y^Tb \leq -1, y\geq 0$. Unfortunately, this will lead to a bilinear model when you parameterize$b(z)$. It is fairly similar to an application I worked on a decade ago Oops! I cannot do it again: Testing for ... 6 You need to introduce a binary variable for buying,$b$, and one for selling,$s$. Make sure$b$and$s$are active when$varBuyWater$and$varSellWater$are positive, respectively: $$varBuyWater \le M_1 b \\ varSellWater \le M_2 s \\$$$M_1$and$M_2$are upper bounds on variables$varBuyWater$and$varSellWater\$. And impose that both binaries cannot ...

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