An Existence Result for the Generalized Vector Equilibrium Problem on Hadamard Manifold

TL;DR

This paper establishes a sufficient condition for the existence of solutions to the generalized vector equilibrium problem on Hadamard manifolds, extending to various optimization and equilibrium problems.

Contribution

It introduces a new existence theorem for GVEP on Hadamard manifolds using a specialized KKM lemma, applicable to multiple problem types.

Findings

Existence condition for GVEP on Hadamard manifolds.

Extension of results to optimization, Nash equilibria, and variational inequalities.

Utilization of a KKM lemma in the manifold context.

Abstract

A sufficient condition for the existence of a solution for generalized vector equilibrium problem (GVEP) on Hadamard manifold, by using a version of KKM lemma on this context, is presented in this paper. It is worth to point out that, in particular, existence result of solution for optimization problems, vector optimization problems, Nash equilibria problems, complementarity problems and variational inequality problems can be obtained as a special case of the existence result for GVEP in this new context.