A theory of “discrete convex analysis” is developed for integer-valued functions defined on
integer lattice points. The theory parallels the ordinary convex analysis, covering discrete …

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 …

Recent years have seen a growing interest in accelerating optimization algorithms with
machine-learned predictions. Sakaue and Oki (NeurIPS 2022) have developed a general …

Abstract M^ ♮ M♮-concave functions form a class of discrete concave functions in discrete
convex analysis, and are defined by a certain exchange axiom. We show in this paper that …

This paper is concerned with algorithms and applications of decreasing minimization on an
M-convex set, which is the set of integral elements of an integral base-polyhedron. Based on …

We study a convex resource allocation problem in which lower and upper bounds are
imposed on partial sums of allocations. This model is linked to a large range of applications …

In discrete convex analysis, the scaling and proximity properties for the class of L^ ♮♮-
convex functions were established more than a decade ago and have been used to design …

In the resource allocation problem (RAP), the goal is to divide a given amount of a resource
over a set of activities while minimizing the cost of this allocation and possibly satisfying …

We continue to consider the discrete decreasing minimization problem on an integral base-
polyhedron treated in Part I. The problem is to find a lexicographically minimal integral …

M ${}^{\natural} $-concave functions, aka gross substitute valuation functions, play a
fundamental role in many fields, including discrete mathematics and economics. In practice …