Strong Convergence in Hilbert Spaces via [Gamma]-Duality

We analyze a primal-dual pair of problems generated via a duality theory introduced by Svaiter. We propose a general algorithm and study its convergence properties. The focus is a general primal-dual principle for strong convergence of some classes of algorithms. In particular, we give a different v...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 158; no. 2; p. 343
Main Authors Marques Alves, M, Melo, J G
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.08.2013
Subjects
Algorithms
Analysis
Convergence
Game theory
Hilbert space
Linear programming
Methods
Number systems
Optimization
Partial differential equations
Studies
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Summary:We analyze a primal-dual pair of problems generated via a duality theory introduced by Svaiter. We propose a general algorithm and study its convergence properties. The focus is a general primal-dual principle for strong convergence of some classes of algorithms. In particular, we give a different viewpoint for the weak-to-strong principle of Bauschke and Combettes and unify many results concerning weak and strong convergence of subgradient type methods.[PUBLICATION ABSTRACT]
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-012-0253-9