Strict Feasibility And Solvability Of Variational Inequality Problems

This paper mainly studies the relationship of strict feasibility and solvability for variational inequality problem. Firstly, we investigate the relationship of strict feasibility and solvability for the variational inequality problem with quasimonotone mappings. We derive that the variational inequality problem is solvable whenever it is strictly feasible under suitable conditions. Secondly, we investigate the relationship of strict feasibility and solvability for the multivalued vector variational inequality problem with quasimonotone mappings. Finally, We prove the existence of the Stampacchia variational inequality for a qusimonotone multivalued operator in locally convex topological vector spaces.