Iterative Algorithms for Equilibrium Problems
We consider equilibrium problems in the framework of the formulation proposed by Blum and Oettli, which includes variational inequalities, Nash equilibria in noncooperative games, and vector optimization problems, for instance, as particular cases. We show that such problems are particular instances...
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| Published in | Optimization Vol. 52; no. 3; pp. 301 - 316 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis Group
01.06.2003
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| Subjects | |
| Online Access | Get full text |
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| Abstract | We consider equilibrium problems in the framework of the formulation proposed by Blum and Oettli, which includes variational inequalities, Nash equilibria in noncooperative games, and vector optimization problems, for instance, as particular cases. We show that such problems are particular instances of convex feasibility problems with infinitely many convex sets, but with additional structure, so that projection algorithms for convex feasibility can be modified in order to improve their convergence properties, mainly achieving global convergence without either compactness or coercivity assumptions. We present a sequential projections algorithm with an approximately most violated constraint control strategy, and two variants where exact orthogonal projections are replaced by approximate ones, using separating hyperplanes generated by subgradients. We include full convergence analysis of these algorithms. |
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| AbstractList | We consider equilibrium problems in the framework of the formulation proposed by Blum and Oettli, which includes variational inequalities, Nash equilibria in noncooperative games, and vector optimization problems, for instance, as particular cases. We show that such problems are particular instances of convex feasibility problems with infinitely many convex sets, but with additional structure, so that projection algorithms for convex feasibility can be modified in order to improve their convergence properties, mainly achieving global convergence without either compactness or coercivity assumptions. We present a sequential projections algorithm with an approximately most violated constraint control strategy, and two variants where exact orthogonal projections are replaced by approximate ones, using separating hyperplanes generated by subgradients. We include full convergence analysis of these algorithms. |
| Author | Sosa, Wilfredo Iusem, Alfredo N. |
| Author_xml | – sequence: 1 givenname: Alfredo N. surname: Iusem fullname: Iusem, Alfredo N. organization: Instituto de Matemática Pura e Aplicada – sequence: 2 givenname: Wilfredo surname: Sosa fullname: Sosa, Wilfredo organization: Instituto de Matemática y Ciencias Afines |
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| SubjectTerms | Convex Feasibility Problems Equilibrium Problems Mathematics Subject Classification 2000: 49m37 Projection Methods |
| Title | Iterative Algorithms for Equilibrium Problems |
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