Hybrid proximal methods for equilibrium problems |
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Authors: | Boris S. Mordukhovich Barbara Panicucci Massimo Pappalardo Mauro Passacantando |
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Affiliation: | 1. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA 2. Department of Applied Mathematics, University of Pisa, via Buonarroti 1/c, 56127, Pisa, Italy
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Abstract: | This paper concerns developing two hybrid proximal point methods (PPMs) for finding a common solution of some optimization-related problems. First we construct an algorithm to solve simultaneously an equilibrium problem and a variational inequality problem, combing the extragradient method for variational inequalities with an approximate PPM for equilibrium problems. Next we develop another algorithm based on an alternate approximate PPM for finding a common solution of two different equilibrium problems. We prove the global convergence of both algorithms under pseudomonotonicity assumptions. |
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