Fundamental Properties of M-Convex and L-Convex Functions in Continuous Variables
Fundamental Properties of M-Convex and L-Convex Functions in Continuous Variables
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发表时间：
2004-05
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通讯作者：
K. Murota;A. Shioura
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作者：
K. Murota;A. Shioura
Murota（1996，1998）针对整数格上的函数引入了M-凸性和L-凸性的概念，它们提取了非线性组合优化问题的组合结构. Murota{Shioura（2000，2001）将这些概念推广到真实的空间上的多面体凸函数和二次函数。在本文中，我们考虑一般凸函数的进一步推广。本文的主要目的是给出一般M-凸函数和L-凸函数的基本性质的严格证明。
The concepts of M-convexity and L-convexity, introduced by Murota (1996,1998) for functions on the integer lattice, extract combinatorial structures in well-solved nonlinear combinatorial optimization problems. These concepts are extended to polyhedral convex functions and quadratic functions on the real space by Murota{Shioura (2000, 2001). In this paper, we consider a further extension to general convex functions. The main aim of this paper is to provide rigorous proofs for fundamental properties of general M-convex and L-convex functions.