Iusem, Alfredo N.; Sosa, Wilfredo Iterative algorithms for equilibrium problems. (English) Zbl 1176.90640 Optimization 52, No. 3, 301-316 (2003). Summary: 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. Cited in 4 ReviewsCited in 87 Documents MSC: 90C47 Minimax problems in mathematical programming 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 49J40 Variational inequalities 49M37 Numerical methods based on nonlinear programming 65K05 Numerical mathematical programming methods Keywords:Equilibrium Problems; Convex Feasibility Problems; Projection Methods PDF BibTeX XML Cite \textit{A. N. Iusem} and \textit{W. Sosa}, Optimization 52, No. 3, 301--316 (2003; Zbl 1176.90640) Full Text: DOI OpenURL