Problemas de equilíbrio e quase-equilíbrio: uma abordagem teórica e numérica

Abstract

[EN] In this work we present an existence result of solution for the quasi-equilibrium problems (QEP) in Banach spaces using the generalized KKM theory, without compactness assumption on the constrained set. As application we obtain existence results for quasi-variational inequalities and generalized Nash equilibrium problems. We report some examples and comparisons with other problems existent in the literature. Moreover, in this work we develop a Quasi-Newton type method for equilibrium problems based on the proximal Newton-type structure given in Santos et al. (Optimization Letters 12(5)997-1009, 2018). We consider a family of matrices verifying the bounded deterioration property. We prove the well definition of the proposed method and under suitable assumptions we establish the linear convergence of the algorithm. Futhermore, numerical experiments are reported.