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On the nonemptiness and compactness of the solution sets for vector variational inequalities. (English) Zbl 1229.90231
Summary: We investigate conditions for nonemptiness and compactness of the sets of solutions of pseudomonotone vector variational inequalities by using the concept of asymptotical cones. We show that a pseudomonotone vector variational inequality has a nonempty and compact solution set provided that it is strictly feasible. We also obtain some necessary conditions for the set of solutions of a pseudomonotone vector variational inequality to be nonempty and compact.
MSC:
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)