Journal of Inequalities and Applications
Volume 2 (1998), Issue 2, Pages 157-179

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

Copyright © 1998 Z. Wel et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.