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Convergence Analysis of Some Methods for Minimizing a Nonsmooth Convex Function (1998)

Abstract

In this paper, we analyze a class of methods for minimizing a proper lower semicontinuous extended-valued convex function . Instead of the original objective function f , we employ a convex approximation f k + 1 at the k th iteration. Some global convergence rate estimates are obtained. We illustrate our approach by proposing (i) a new family of proximal point algorithms which possesses the global convergence rate estimate even it the iteration points are calculated approximately, where are the proximal parameters, and (ii) a variant proximal bundle method. Applications to stochastic programs are discussed.. Peer Reviewed. http://deepblue.lib.umich.edu/bitstream/2027.42/45249/1/10957_2004_Article_417694.pdf

Publication details

Download	, http://hdl.handle.net/2027.42/45249 http://www.ncbi.nlm.nih.gov/sites/entrez?cmd=retrieve&db=pubmed&list_uids=12168037&dopt=citation
Publisher	Kluwer Academic Publishers-Plenum Publishers; Plenum Publishing Corporation ; Springer Science+Business Media
Contributors	Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan, School of Mathematics, University of New South Wales, Sydney, NSW, Australia, School of Mathematics, University of New South Wales, Sydney, NSW, Australia, Ann Arbor
Repository	University of Michigan (United States)
Keywords	stochastic programming, Mathematics, Theory of Computation, Applications of Mathematics, Calculus of Variations and Optimal Control, Engineering, general, Nonsmooth convex optimization, proximal point method, bundle algorithm, Optimization, Operation Research/Decision Theory, Optimization, Mathematics, Science
Language	English

Cited publications (3)

Proximité et dualité dans un espace hilbertien (1965)

Moreau, J.J.

Partial proximal minimization algorithms for convex programming (1993)

Methods of descent for nondifferentiable optimization / Krzysztof C. Kiwiel (1985)