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2005•Unpublished venueRequires access

Equilibrium programming in Hilbert spaces

Patrick L. Combettes, Sever A. Hirstoaga

Open publisher page 929 citations

Abstract

Several methods for solving systems of equilibrium problems in Hilbert spaces – and for find-ing best approximations thereof – are presented and their convergence properties are established. The proposed methods include proximal-like block-iterative algorithms for general systems, as well as regularization and splitting algorithms for single equilibrium problems. The problem of constructing approximate equilibria in the case of inconsistent systems is also considered. 1

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What this paper is about

Several methods for solving systems of equilibrium problems in Hilbert spaces – and for find-ing best approximations thereof – are presented and their convergence properties are established. The proposed methods include proximal-like block-iterative algorithms for general systems, as well as regularization and splitting algorithms for single equilibrium problems. The problem of constructing approximate equilibria in the case of inconsistent systems is also considered. 1

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OpenAlex reports 929 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Several methods for solving systems of equilibrium problems in Hilbert spaces – and for find-ing best approximations thereof – are presented and their convergence properties are established. The proposed methods include proximal-like block-iterative algorithms for general systems, as well as regularization and splitting algorithms for single equilibrium problems. The problem of constructing approximate equilibria in the case of inconsistent systems is also considered. 1

Key concepts: Hilbert space, Convergence (economics), Mathematics, Regularization (linguistics), Mathematical optimization, Block (permutation group theory), Applied mathematics, Algorithm

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