A General Approach to Convergence Properties of Some Methods for Nonsmooth Convex Optimization
dc.contributor.author | Birge, John R. | en_US |
dc.contributor.author | Wei, Zengxin | en_US |
dc.contributor.author | Qi, Liqun | en_US |
dc.date.accessioned | 2006-09-08T20:16:18Z | |
dc.date.available | 2006-09-08T20:16:18Z | |
dc.date.issued | 1998-0910 | en_US |
dc.identifier.citation | Birge, J. R.; Qi, L.; Wei, Z.; (1998). "A General Approach to Convergence Properties of Some Methods for Nonsmooth Convex Optimization ." Applied Mathematics & Optimization 38(2): 141-158. <http://hdl.handle.net/2027.42/42374> | en_US |
dc.identifier.issn | 0095-4616 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/42374 | |
dc.description.abstract | Based on the notion of the ε -subgradient, we present a unified technique to establish convergence properties of several methods for nonsmooth convex minimization problems. Starting from the technical results, we obtain the global convergence of: (i) the variable metric proximal methods presented by Bonnans, Gilbert, Lemaréchal, and Sagastizábal, (ii) some algorithms proposed by Correa and Lemaréchal, and (iii) the proximal point algorithm given by Rockafellar. In particular, we prove that the Rockafellar—Todd phenomenon does not occur for each of the above mentioned methods. Moreover, we explore the convergence rate of { ||x k || } and {f(x k ) } when {x k } is unbounded and {f(x k ) } is bounded for the non-smooth minimization methods (i), (ii), and (iii). | en_US |
dc.format.extent | 156589 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Springer-Verlag; Springer-Verlag New York Inc. | en_US |
dc.subject.other | Key Words. Nonsmooth Convex Minimization, Global Convergence, Convergence Rate. AMS Classification. 90C25, 90C30, 90C33. | en_US |
dc.subject.other | Legacy | en_US |
dc.title | A General Approach to Convergence Properties of Some Methods for Nonsmooth Convex Optimization | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Industrial and Operations Engineering | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Engineering | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI 48109, USA , US, | en_US |
dc.contributor.affiliationother | School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia , AU, | en_US |
dc.contributor.affiliationother | School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia , AU, | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/42374/1/245-38-2-141_38n2p141.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/s002459900086 | en_US |
dc.identifier.source | Applied Mathematics & Optimization | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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