A new method for nonsmooth convex optimization. Issue 2 (1998)

• Record Type: Journal Article
• Authors: Wel, Z.; Qi, L.; Birge, J. R.
• Is Part Of: Journal of inequalities and applications. Volume 2:Issue 2(1998)
• Page Start: 157
• Page End: 179
• Publication Date: 1998
• Subjects: Proper closed convex function; Proximal minimization; Global and superlinear convergence; Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/S1025583498000101
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : A new method for minimizing a proper closed convex functionf is proposed and its convergence properties are studied. The convergence rate depends on both the growth speed offf 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.