  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 generalized
linear programming problems and generalized linear vector optimization problems
are shown.
