A Sequential Quadratic Programming Method for Nonsmooth Optimization

Algorithms for the solution of smooth, constrained optimization problems have enjoyed great successes in recent years. In particular, the framework known as sequential quadratic programming (SQP) has been studied and applied to a variety of interesting applications. Similarly, there has been a great deal of recent work on the solution of nonsmooth, unconstrained optimization applications. One approach that has been successful in this context is gradient sampling (GS) — a method that, unlike the many variations of bundle methods, only requires the computation of gradients during the solution process. In this talk, we combine elements of SQP and GS to create an algorithm for nonsmooth, constrained optimization and illustrate the potential for such an approach on illustrative test problems in eigenvalue optimization and compressed sensing.