Duality in convex optimization, via perturbation arguments

Abstract: Sometimes optimization problems are hard. One method for attacking difficult problems is to pass to a dual formulation of the problem, solve this (potentially easier) dual problem, and then recover a solution to your original problem. In this talk, we will discuss how the duality method can be interpreted in terms of the sensitivity of solutions to perturbations in problem parameters. A traditional perturbation yields the classical Lagrange duality, and new work shows that a different choice of perturbation leads to the less-studied gauge duality.

No optimization background will be assumed.