Short Proofs of the Separation Theorems for L-convex/concave and M-convex/concave Functions
نویسندگان
چکیده
Recently K. Murota has introduced concepts of L-convex function and Mconvex function as generalizations of those of submodular function and base polyhedron, respectively, and has shown separation theorems for L-convex/concave functions and for M-convex/concave functions. The present note gives short alternative proofs of the separation theorems by relating them to the ordinary separation theorem in convex analysis with the full use of recently obtained knowledge about L-/M-convex functions.
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