Abstract.
The concepts of L-convex function and M-convex function have recently been introduced by Murota as generalizations of submodular function and base polyhedron, respectively, and discrete separation theorems are established for L-convex/concave functions and for M-convex/concave functions as generalizations of Frank’s discrete separation theorem for submodular/supermodular set functions and Edmonds’ matroid intersection theorem. This paper shows the equivalence between Murota’s L-convex functions and Favati and Tardella’s submodular integrally convex functions, and also gives alternative proofs of the separation theorems that provide a geometric insight by relating them to the ordinary separation theorem in convex analysis.
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Received: November 27, 1997 / Accepted: December 16, 1999¶Published online May 12, 2000
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Fujishige, S., Murota, K. Notes on L-/M-convex functions and the separation theorems. Math. Program. 88, 129–146 (2000). https://doi.org/10.1007/PL00011371
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DOI: https://doi.org/10.1007/PL00011371