Lecture 7: Example: Piecewise Linear Minimization

Doesn’t really matter what it is. You find the analytic center of the polyhedron, which is to say more precisely, you find the analytic center of the linear inequalities that represent the polyhedron. And you query the cutting-plane oracle at that point. If that point is in your target set, you quit. Otherwise, you add, you append this new cutting-plane to the set. Of course, what happens now is your point X (K+1) is not in P (K+1) by definition. Well, sorry. It might be in it if it’s a neutral cut, but it’s on the boundary. ... See the whole transcript at [[http://see.stanford.edu/materials/lsocoee364b/transcripts/ConvexOptimizationII-Lecture07.pdf|Convex Optimization II - Lecture 07]]