10 citations · 45 across the 35 of their papers we have counts for
35 papers
Quiver Semistability and Structured Kalman Decompositions for Networked Linear Dynamical Systems
Kazuo Murota, Tasuku Soma
We introduce new notions of controllability and observability for networked linear time-invariant (LTI) systems based on -semistability of quiver representations. Utilizing King…
Note on Steepest Descent Algorithm for Quasi L-convex Function Minimization
Kazuo Murota, Akiyoshi Shioura
We define a class of discrete quasi convex functions, called semi-strictly quasi L-convex functions, and show that the steepest descent algorithm for L-co…
Decomposition of an Integrally Convex Set into a Minkowski Sum of Bounded and Conic Integrally Convex Sets
Kazuo Murota, Akihisa Tamura
Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar statements for some classes of…
Note on Minimization of Quasi M-convex Functions
Kazuo Murota, Akiyoshi Shioura
For a class of discrete quasi convex functions called semi-strictly quasi M-convex functions, we investigate fundamental issues relating to minimization, such as optimal…
Shapley-Folkman-type Theorem for Integrally Convex Sets
Kazuo Murota, Akihisa Tamura
The Shapley-Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This p…
Double-Exponential transformation: A quick review of a Japanese tradition
Kazuo Murota, Takayasu Matsuo
This paper is a short introduction to numerical methods using the double exponential (DE) transformation, such as tanh-sinh quadrature and DE-Sinc approximation. The DE-based metho…
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…
Recent Progress on Integrally Convex Functions
Kazuo Murota, Akihisa Tamura
Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims…
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…
Inclusion and Intersection Relations Between Fundamental Classes of Discrete Convex Functions
Satoko Moriguchi, Kazuo Murota
In discrete convex analysis, various convexity concepts are considered for discrete functions such as separable convexity, L-convexity, M-convexity, integral convexity, and multimo…
Note on the Polyhedral Description of the Minkowski Sum of Two L-convex Sets
Satoko Moriguchi, Kazuo Murota
L-convex sets are one of the most fundamental concepts in discrete convex analysis. Furthermore, the Minkowski sum of two L-convex sets, called L2-convex sets, is an intriguing obj…
Discrete Fenchel Duality for a Pair of Integrally Convex and Separable Convex Functions
Kazuo Murota, Akihisa Tamura
Discrete Fenchel duality is one of the central issues in discrete convex analysis. The Fenchel-type min-max theorem for a pair of integer-valued M-natural-convex functions generali…
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…
Fair Integral Submodular Flows
András Frank, Kazuo Murota
Integer-valued elements of an integral submodular flow polyhedron are investigated which are decreasingly minimal (dec-min) in the sense that their largest component is as smal…
Decreasing Minimization on M-convex Sets: Algorithms and Applications
András Frank, Kazuo Murota
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…
Decreasing Minimization on M-convex Sets: Background and Structures
András Frank, Kazuo Murota
The present work is the first member of a pair of papers concerning decreasingly-minimal (dec-min) elements of a set of integral vectors, where a vector is dec-min if its largest c…
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…
On Basic Operations Related to Network Induction of Discrete Convex Functions
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 investigate b…
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…
Fair Integral Network Flows
András Frank, Kazuo Murota
A strongly polynomial algorithm is developed for finding an integer-valued feasible -flow of given flow-amount which is decreasingly minimal on a specified subset of edges…
Discrete Decreasing Minimization, Part II: Views from Discrete Convex Analysis
András Frank, Kazuo Murota
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 v…
Discrete Decreasing Minimization, Part I: Base-polyhedra with Applications in Network Optimization
András Frank, Kazuo Murota
Borradaile et al. (2017) investigated orientations of an undirected graph in which the sequence of in-degrees of the nodes is lexicographically minimal, which we call decreasingly…
Integrality of Subgradients and Biconjugates of Integrally Convex Functions
Kazuo Murota, Akihisa Tamura
Integrally convex functions constitute a fundamental function class in discrete convex analysis. This paper shows that an integer-valued integrally convex function admits an integr…