Journal of Inequalities and Applications 
Volume 2 (1998), Issue 2, Pages 157-179
doi:10.1155/S1025583498000101

A new method for nonsmooth convex optimization

Z. Wel,1 L. Qi,1 and J. R. Birge2

 1School of Mathematics, University of New South Wales, Sydney 2052, NSW, Australia
2Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor 48109, MI, USA
Received 3 March 1997

Abstract

A new method for minimizing a proper closed convex function f is proposed and its convergence properties are studied. The convergence rate depends on both the growth speed off f at minimizers and the choice of proximal parameters. An application of the method extends the corresponding results given by Kort and Bertsekas for proximal minimization algorithms to the case in which the iteration points are calculated approximately. In particular, it relaxes the convergence conditions of Rockafellar’s results for the proximal point algorithm.