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 ...
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 ...
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 ...
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 ...
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 ...
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