We consider equilibrium constrained optimization problems, which have a general formulation that encompasses well-known models such as mathematical programs with equilibrium constraints, bilevel programs, and generalized semi-infinite programming problems. Based on the celebrated KKM lemma, we prove the existence of feasible points for the equilibrium constraints. Moreover, we analyze the topol...

In this work, we study the following Generalized Variational Inequality Problem (for short, GVIP): Given a closed convex set K in a reflexive Banach space E with the dual E, a multifunction T : K → 2E∗ , and a vector b ∈ E, find x̄ ∈ K such that there exists ū ∈ T(x̄) satisfying 〈ū− b, y− x̄〉 ≥ 0, for all y ∈ K. By using generalized projection and the well-known Fan–KKM Theorem, we prove existence...