0

I have a system of linear inequalities $Ax \leq b$. It is possible that some inequality constraints actually create a linear equality constraint. for e.g. $ax \leq b$ and $ax \geq b$ implies $ax=b$. A more involved linear combination of inequalities can also lead to equality constraints. I want to detect the final equality constraint given that $Ax \leq b$. Can it be done ?

user402940
  • 381

1 Answers1

0

Exactly checking for $a^Tx\le b$ and $-a^Tx\le -b$ can be done efficiently with hashing. But what about $\alpha a^Tx\le \alpha b$. You could normalize (scale) first but then you would need to apply some tolerance. I don't think standard LP preprocessors will check for this (other reductions are more important).

Erwin Kalvelagen
  • 4,267
  • Yeah, thats true. Even scaling/normalizing issues can be resolved with little computational effort. However when a collection of inequalities imply a equality its very hard to detect. Is there a standard way ? – user402940 Nov 14 '17 at 05:11