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.

Hybrid proximal methods for equilibrium problems

PAPPALARDO, MASSIMO;PASSACANTANDO, MAURO
2012-01-01

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.
2012
Mordukhovich, Boris S.; Panicucci, Barbara; Pappalardo, Massimo; Passacantando, Mauro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/191196
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