# How to linearise a quadratic constraint????

 1 There is a decision variable $$x \ge 0$$ and a given parameter $$\text{MIN}$$. The quantity $$mk$$ is calculated as $$mk = \text{MIN} - x$$. I want to distinguish cases as far as the sign of $$mk$$ is concerned. I have defined a binary decision variable that is $$1$$ when $$mk \ge 0$$ and $$0$$ otherwise. I have the following constraint $$y \le \text{A} + b \cdot mk$$. $$\text{A}$$ is a parameter/constant. How can I linearize it? Thanks in advance, Standrul asked 24 Nov '11, 08:13 standrul 13●1●3 accept rate: 0% fbahr ♦ 4.6k●7●16 Is b a decision variable? How does it fit with the rest? (24 Nov '11, 08:16) Thiago Serra Sorry! Yes b is the binary decision var I defined that is 1 when mk>=0 and 0 otherwise. (24 Nov '11, 08:21) standrul

 2 Assuming you have an upper bound $$U$$ on $$x$$: $$y \le A+mk-(1-b) \times (MIN-U)$$ and $$y \le A+b \times MIN$$ answered 25 Nov '11, 17:15 Paul Rubin ♦♦ 14.6k●5●13 accept rate: 19% fbahr ♦ 4.6k●7●16
 1 From AIMMS' Modeling Guide, chapter on "Integer Programming Tricks": answered 24 Nov '11, 09:50 fbahr ♦ 4.6k●7●16 accept rate: 13%
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