Bundle Methods For A Class Of Nonconvex Nonsmooth Optimization

Proximal bundle methods are very successful for solving unconstrained convex pro-gramming, and they can also be extended to nonconvex case by modifying the convex forerunner. Here we turn to constrained nonconvex nonsmooth optimization. Little sys-tematic research has been made on this because both objective and constraint functions may not be convex. This work first transforms this problem into unconstrained one with the help of exact penalty function and certifies the existence of exact penalty parameter through adding some constraint qualifications. Then for the nonconvexity we apply local convexihation of the penalty function, and that leads bundle method workable. The sequence generated by our algorithm is proved to be convergent at KKT points of the primal problem under certain assumptions. Finally some illustrative examples are given to show how this method works.