Sign of a Linear Expression in Mixed Integer Linear ProgrammingI have a question about a system in mixed integer programming I am trying to solve using GLPK though the question mathematical and is software agnostic.I have converted the whole problem to linear equations and inequalities except for one part. Suppose I have a real number x and a binary variable b (either 0 or 1). How can I "tie them together" such that x &gt; 0 if and only if b = 1?

Question

Sign of a Linear Expression in Mixed Integer Linear ProgrammingI have a question about a system in mixed integer programming I am trying to solve using GLPK though the question mathematical and is software agnostic.I have converted the whole problem to linear equations and inequalities except for one part. Suppose I have a real number   x and a binary variable   b (either 0 or 1). How can I &quot;tie them together&quot; such that   x  &amp;gt;  0 if and only if   b  =  1?

Ordettyreomqu · Accepted Answer

0.001  b  ≤  x  ≤  U  bwhere I assume   0  ≤  x  ≤  U.I don&#039;t see how this particular formulation is related to NP-completeness. If you are worried about the complexity of this don&#039;t use a MIP model at all but rather use a heuristic (even this may be overstating things as state-of-the-art MIP solvers actually use lots of heuristics internally).