Conjugacy relationship between M-convex and L-convex functions in continuous variables |
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| Authors: | Kazuo Murota Akiyoshi Shioura |
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| Institution: | (1) Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan;(2) Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan;(3) PRESTO, JST, Tokyo, Japan |
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| Abstract: | By extracting combinatorial structures in well-solved nonlinear combinatorial optimization problems, Murota (1996,1998) introduced the concepts of M-convexity and L-convexity to functions defined over the integer lattice. Recently, Murota–Shioura (2000, 2001) extended these concepts to polyhedral convex functions and quadratic functions in continuous variables. In this paper, we consider a further extension to more general convex functions defined over the real space, and provide a proof for the conjugacy relationship between general M-convex and L-convex functions.Mathematics Subject Classification (1991): 90C10, 90C25, 90C27, 90C35This work is supported by Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan |
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| Keywords: | combinatorial optimization matroid base polyhedron convex function convex analysis |
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