2 citations · 3 across the 7 of their papers we have counts for
10 papers · 1 filter
Discrete Convex Analysis: A Tool for Economics and Game Theory
Kazuo Murota
This paper presents discrete convex analysis as a tool for economics and game theory. Discrete convex analysis is a new framework of discrete mathematics and optimization, develope…
Decreasing Minimization on Base-Polyhedra: Relation Between Discrete and Continuous Cases
András Frank, Kazuo Murota
This paper is concerned with the relationship between the discrete and the continuous decreasing minimization problem on base-polyhedra. The continuous version (under the name of l…
Exchange Properties of M-natural-concave Set Functions and Valuated Matroids
Kazuo Murota
This is a survey article on the exchange properties characterizing M-natural-concave set functions and valuated matroids (M-concave set functions). The objective of this paper is t…
A Discrete Convex Min-Max Formula for Box-TDI Polyhedra
András Frank, Kazuo Murota
A min-max formula is proved for the minimum of an integer-valued separable discrete convex function where the minimum is taken over the set of integral elements of a box total dual…
A Survey of Fundamental Operations on Discrete Convex Functions of Various Kinds
Kazuo Murota
Discrete convex functions are used in many areas, including operations research, discrete-event systems, game theory, and economics. The objective of this paper is to offer a surve…
A Note on M-convex Functions on Jump Systems
Kazuo Murota
A jump system is defined as a set of integer points (vectors) with a certain exchange property, generalizing the concepts of matroids, delta-matroids, and base polyhedra of integra…