Lecture 4: Project Subgradient For Dual Problem

Sure, we’re going to need strong duality holds if it were strictly feasible. We’d have Slater’s condition and strong duality would hold. That gives you zero duality gap and I guess if you don’t have that, then you can’t solve this at all, because the optimal values aren’t even the same. So let’s assume that. There’s more, actually, to it than just that. What the sledgehammer condition is is this. What you’ll need is that when you find lambda*, what you want is that the Lagrangian at lambda* should have a unique minimizer in x. If it does, then that x is actually x* up here. Okay? So that’s the condition. ... See the whole transcript at [[http://see.stanford.edu/materials/lsocoee364b/transcripts/ConvexOptimizationII-Lecture04.pdf|Convex Optimization II - Lecture 04]]