I am looking for a way to express an "or" option in a system of...
I am looking for a way to express an "or" option in a system of linear inequalities for a linear program I am working on.
I will explain what I mean precisely: Lets say I have a set of inequalities to , which must hold. But, additionally, I have several more inequalities and , that can be partitioned to couples (of the form for all ), such that either holds or if it doesn't then . Nonetheless, it is also possible for both of them to hold. What I am looking for is an option to encode such an "or" condition on a set of inequalities.
Ofcourse, if we say that is lets say and is I can write , but this demand is too strong, because in my original problem I may allow (for example) as long as g(...)≤M, but then . So requiring is too strong for me.
My question can be divided to 2 questions:
1. Is there any idea for a nice trick here or for some sort of a reduction to Linear Programming?
2. Perhaps there exists a software or an online site which allow this kind of "or"?