tilon solving non-linear programming problems

Given 2 valid models, A and B, for a non-LP problem, and you want to minimize solution time:

• Each model has an integer space flesh, (convex hull) which is searched through with Branch & Bound

• Each model also has a “crust”, which is what happens when you relax the constraints to become an LP.

  • Let’s call it A_lp, B_lp

• The crust is useless search space that takes up time in the branch and bound, therefore we should try to minimize it. However, solving linear programming is easy.

• You can minimize it by:

  • Proving A_lp is a subset of B_lp, then choose (A) as your model

  • Proving B_lp is a subset of A_lp, then choose (B) as your model

  • If neither of these are the case, then choose (A intersect B) as your model