Time: 9h00, Wednesday, November 11, 2015
Location: Room 4, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract:  It is well known that finite-dimensional polyhedral convex sets can be generated by finitely many points and finitely many directions. Representation formulas in this spirit are obtained for convex polyhedra and generalized convex polyhedra in locally convex Hausdorff topological vector spaces. Our results develop those of X.Y.Zheng (Set-Valued Anal., Vol. 17, 2009, 389--408), which were established in a Banach space setting. Applications of the representation formulas to proving solution existence theorems for infinite-dimensional linear programming problems and infinite-dimensional linear vector optimization problems are shown.