Simplification of solution graph strategy

[forrestlaine]

Let A be a subset of B S = (x,w) : x solves min_x f(x,w) s.t. (x,w) in A T = (x,w) : x solves min_x f(x,w) s.t. (x,w) in B

T intersect A is a subset of S If T is a subset of A, T = S

Strategy: -Form good over-approx of A = union of polys (call it B) -Find T -Check T is a subset of A (this is hard in general but I think this can be proven to be fast given the form of A,B -If subset, then T = S. Else, refine. -What does refine mean?

[forrestlaine]

todo: check whether the convex hull of polyhedral projections == polyhedral projection of convex hull