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.
Number in Series
Applied Mathematics | Mathematics
Mordukhovich, Boris S.; Panicucci, Barbara; Passacantando, Mauro; and Pappalardo, Massimo, "Hybrid Proximal Methods for Equilibrium Problems" (2009). Mathematics Research Reports. 70.