On the methods of nonsmooth optimization

Abstract

In this paper we shall give a short derivation of the most promising methods in nonsmooth optimization, namely bundle methods. We introduce the basic bundle idea due to Lemarechal and several modifications by Kiwiel, Schramm and Zowe. To the end we shall give some numerical results comparing the efficience of these methods. As test problems we have used well-known test problems from litterature and in addition we shall give some contributions to nonsmooth optimal control problems.