We study the class of Lorentzian polynomials. The class contains homogeneous stable
polynomials as well as volume polynomials of convex bodies and projective varieties. We …

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 describes recent developments in discrete convex analysis. Particular emphasis
is laid on natural introduction of the classes of L-convex and M-convex functions in 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 …

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 survey …

Multimodular functions, primarily used in the literature of queueing theory, discrete-event
systems, and operations research, constitute a fundamental function class in discrete convex …

We consider the problem of making a given (k− 1)-connected graph k-connected by adding
a minimum number of new edges, which we call the k-connectivity augmentation problem. In …

In the optimal general factor problem, given a graph G=(V, E) and a set B (v)⊆ Z of integers
for each v∈ V, we seek for an edge subset F of maximum cardinality subject to d F (v)∈ B …

The class of gross substitutes (GS) set functions plays a central role in Economics and
Computer Science. GS belongs to the hierarchy of complement free valuations introduced …

In this paper, we consider the problem of finding a maximum weight 2-matching containing
no cycle of a length of at most three in a weighted simple graph, which we call the weighted …