7 votes

In linear programming, is there a way to constrain two variables to not have opposite sign

I don't think it is possible in general. If we introduce variables $t_i$, we can write the problem as: $\max ...$ s.t. $x_i \ge t_i$ $ y_i \ge 0 $ $ x_{min} \le t_i \le 0 $ $ y_it_i = 0 $ (this ...
Thijs Steel's user avatar
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3 votes

In linear programming, is there a way to constrain two variables to not have opposite sign

When we "Plot" the region covered by a Pair of $(x,y)$ variables , we can see that it is Non-Convex , hence Linear Programming can not work out. With that Point , we have couple of ...
Prem's user avatar
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3 votes
Accepted

In linear programming, how can I specify a lower bound for the positive entries in the decision vector

You have a disjunctive inequality which may be expressed as $[z=0,x \leq 0] \vee [z=1,x \geq 5]$. This is non-convex, so cannot be expressed as an LP. But as you suggest, there is a way to formulate ...
jdgleeson's user avatar
  • 376
2 votes

In linear programming, how can I specify a lower bound for the positive entries in the decision vector

This is a disjunctive constraint. Some optimization modeling systems/languages and solvers allow you to directly specify constraints as disjunctive, and they will take care of it for you. If not, this ...
Mark L. Stone's user avatar
1 vote

MIP - Large Piecewise Linear Constraints Over Continuous Intervals

You could have a look at the paper from Vielma et al. (https://doi.org/10.1287/opre.1090.0721) to gather more insights on how to represent your function as a piecewise-linear (PWL) model in a MILP ...
Victor Ruela's user avatar

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