About the Links Between Equilibrium Problems and Variational Inequalities

Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for global solutions. Nevertheless, the analysis of such problems found in the literature seems to be very restricted to the global treatment. Motivated by this fact, in this work, we propose local solution concepts, study their interrelations and relations with global concepts and prove existence results as well as stability of local solution map of parametric variational inequalities.The key ingredient of our results is the new concept of local reproducibility of a set-valued map, which we introduce to explore such local solutions to quasivariational inequality problems. As a by-product, we obtain local solutions to quasi-optimization problems, bilevel quasi-optimization problems and Single-Leader-Multi-Follower games.

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About the Links Between Equilibrium Problems and Variational Inequalities

Cited by 5 publications

References 21 publications

An Alternative Extragradient Method for a Vector Quasi-Equilibrium Problem to a Vector Generalized Nash Equilibrium Problem

An Alternative Extragradient Method for a Vector Quasi-Equilibrium Problem to a Vector Generalized Nash Equilibrium Problem

An extragradient algorithm for quasiconvex equilibrium problems without monotonicity

Existence Results for Quasi-variational Inequalities with Applications to Radner Equilibrium Problems

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