Conjugacy relationship between M-convex and L-convex functions in continuous variables
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.
convex function combinatorial optimization matroid base polyhedron convex analysis