A Unified Analysis of Nonconvex Optimization Duality and Penalty Methods with General Augmenting Functions
Asuman Ozdaglar · 2006
In this paper, we study a unifying framework for the analysis of duality schemes and penalty methods constructed using augmenting functions that need not be nonnegative or bounded from below. We consider two geometric optimization problems that are dual to each other and characterize primal-dual problems for which the optimal values of the two problems are equal. To establish this, we show that we can use general concave surfaces to separate nonconvex sets with certain properties. We apply our framework to study augmented optimization duality and general classes of penalty methods without imposing compactness assumptions.