Yokohama Natl Univ, Fac Econ, Hodogaya Ku, Yokohama, Kanagawa 2408501, Japan = 横浜国立大学経済学部
抄録
One of the most important properties of a convex function is that a local optimum is also a global optimum. This paper explores the discrete analogue of this property. We consider arbitrary locality in a discrete space and the corresponding local optimum of a function over the discrete space. We introduce the corresponding notion of discrete convexity and show that the local optimum of a function satisfying the discrete convexity is also a global optimum. The special cases include discretely-convex, integrally-convex, M-convex, W-convex, L-convex, and -convex functions.
雑誌名
Japan Journal of Industrial and Applied Mathematics
A note on discrete convexity and local optimality
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