An outer approximation algorithm for equilibrium problems in Hilbert spaces

We introduce an algorithm for solving non-smooth equilibrium problems in real Hilbert spaces. At each iteration, a regularized proximal-like equilibrium problem on a suitable outer approximation of the original constraint set is considered. We prove, under standard assumptions, that the sequence gen...

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Bibliographic Details
Published in:Optimization methods & software Vol. 30; no. 2; pp. 379 - 390
Main Authors: Santos, P.S.M., Scheimberg, S.
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 04.03.2015
Taylor & Francis Ltd
Subjects:
Algorithms
Approximation
Computer programs
Equilibrium
equilibrium problem
Hilbert space
Mathematical analysis
Mathematical models
Mosco convergence
Optimization
outer approximations
proximal method
Software
ISSN:1055-6788, 1029-4937
Online Access:Get full text
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Summary:We introduce an algorithm for solving non-smooth equilibrium problems in real Hilbert spaces. At each iteration, a regularized proximal-like equilibrium problem on a suitable outer approximation of the original constraint set is considered. We prove, under standard assumptions, that the sequence generated by the algorithm converges weakly to a solution of the problem. Some numerical experience with the algorithm is reported.
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ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2014.961019