Contributions to some equilibrium problems via proximal type algorithms and applications

Abstract

This thesis focuses on the development and analysis of proximal- type algorithms for solving pseudomonotone equilibrium problems in Hilbert and Banach spaces, with application to variational inequalities problems, which is special case of equilibrium problems. Three enhanced algorithms are proposed, incorporating subgradient and extragradient methods with non-monotonic step sizes, along with improvements based on Bregman distance. Weak and strong convergence of these algorithms are established under suitable assumptions. The proposed methods demonstrate significantimprovements in performance, including faster convergence, higher accuracy, and reduced computational time, as confirmed by numerical experiments compared to traditional algorithms.