Abstract:

In modern optimization, many problems take the form of "black-box optimization". In such problem, no analytic information is available, but function values (and possibly gradient values) can be extracted, at great cost, for individual points. One popular method of dealing with these problems is via bundle methods, or the more advanced proximal bundles methods. Although the theory and application of proximal bundle method is well established for convex functions, few attempts have been made to extend these ideas into a nonconvex setting. However recent results on proximal point (the theoretical object upon which proximal bundle methods rely) have suggested that proximal bundle methods should be workable in a nonconvex setting. In these talk we will discuss some of these results, and one new approach for extending classical proximal bundle methods into a nonconvex setting.