Centers of Monotone Generalized Complementarity Problems

Let C be a full dimensional, closed, pointed and convex cone in a finite dimensional real vector space ℰ with an inner product 〈x, y〉 of x, y ∈ ℰ, and ℳ a maximal monotone subset of ℰ × ℰ. This paper studies the existence and continuity of centers of the monotone generalized complementarity problem associated with C and ℳ: Find (x, y) ∈ ℳ ∩ (C × C*) such that 〈x, y〉 = 0. Here C* = {y ∈ ℰ : 〈x, y〉 ≥ 0 for all x ∈ C} denotes the dual cone of C. The main result of the paper unifies and extends some results established for monotone complementarity problems in Euclidean space and monotone semidefinite linear complementarity problems in symmetric matrices.