K. Murota

发表

Convexity and Steinitz's Exchange Property

K. Murota, 1996 .

Systems Analysis by Graphs and Matroids: Structural Solvability and Controllability

K. Murota, 1987 .

Refined study on structural controllability of descriptor systems by means of matroids

K. Murota, 1987 .

Global Convergence of a Modified Newton Iteration for Algebraic Equations

K. Murota, 1982 .

Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10

K. Murota, 2003 .

Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework

Kazuo Murota, Masakazu Kojima, Kazuhide Nakata, 2000, SIAM J. Optim..

Matrices and Matroids for Systems Analysis

Kazuo Murota, K. Murota, 2000 .

Practical use of Bucketing Techniques in Computational Geometry

M. Iri, H. Imai, K. Murota, 1985 .

Block-Triangularizations of Partitioned Matrices under Similarity/Equivalence Transformations

K. Murota, S. Iwata, Hisashi Ito, 1994 .

Structure at infinity of structured descriptor systems and its applications

K. Murota, J. Woude, 1991 .

A numerical algorithm for block-diagonal decomposition of matrix *-algebras with general irreducible components

K. Murota, Takanori Maehara, 2010 .

Group Symmetry in Interior-Point Methods for Semidefinite Program

N. Katoh, K. Murota, Y. Kanno, 2001 .

Mat hemat ical Engineering

Yu. B. Zudin, K. Murota, A. Tamura, 2003 .

Discrete convex analysis: A tool for economics and game theory

K. Murota, 2016, 2212.03598.

M-convex functions and tree metrics

K. Murota, Hiroshito Hira, 2004 .

Some recent results in combinatorial approaches to dynamical systems

K. Murota, 1989 .

Structural solvability of systems of equations —A mathematical formulation for distinguishing accurate and inaccurate numbers in structural analysis of systems—

M. Iri, K. Murota, 1985 .

Use of the concept of physical dimensions in the structural approach to systems analysis

K. Murota, 1985 .

Bifurcation Theory for Hexagonal Agglomeration in Economic Geography

K. Murota, K. Ikeda, 2013 .

The studentized empirical characteristic function and its application to test for the shape of distribution

Kei Takeuchi, Kazuo Murota, K. Takeuchi, 1981 .

NOTE ON THE UNIVERSAL BASES OF A PAIR OF POLYMATROIDS

Kazuo Murota, K. Murota, 1988 .

Comparison of conventional and “invariant” schemes of fundamental solutions method for annular domains

Kazuo Murota, K. Murota, 1995 .

Random Imperfection (I)

K. Murota, K. Ikeda, 2019, Imperfect Bifurcation in Structures and Materials.

Random Imperfection (II)

K. Murota, K. Ikeda, 2019, Imperfect Bifurcation in Structures and Materials.

Abstracts of Workshop on Computational Algebraic Statistics, Theories and Applications

K. Murota, 2008 .

B-371 Scaling Algorithms for M-convex Function Minimization

K. Murota, A. Shioura, Satoko Moriguchi, 2001 .

CHARACTERIZING A VALUATED DELTA-MATROID AS A FAMILY OF DELTA-MATROIDS*

Kazuo Murota, K. Murota, 1997 .

A note on the dqds algorithm with Rutishauser’s shift for singular values

K. Murota, Takayasu Matsuo, Kensuke Aishima, 2011 .

MATHEMATICAL ENGINEERING TECHNICAL REPORTS Note on the Continuity of M-convex and L-convex Functions in Continuous Variables

K. Murota, A. Shioura, 2008 .

M-convex and L-convex Fuctions over the Real Space — Two Conjugate Classes of Combinatorial Convex Functions — 1

K. Murota, A. Shioura, 2002 .

Short Proofs of the Separation Theorems for L-convex/concave and M-convex/concave Functions

Kazuo Murota, Satoru Fujishige, S. Fujishige, 1997 .

Hierarchical decomposition discrete systems by matroid group theories of symmetric and

K. Murota, 1993 .

Decreasing Minimization on M-convex Sets

A. Frank, K. Murota, 2020, 2007.09616.

Discrete Decreasing Minimization, Part II: Views from Discrete Convex Analysis

A. Frank, K. Murota, 2018, 1808.08477.

O C ] 1 1 M ay 2 01 8 On Fundamental Operations for Multimodular Functions ∗

K. Murota, Satoko Moriguchi, 2018 .

Discrete Convex Optimization Solvers and Demonstration Softwares

K. Murota, Satoko Moriguchi, Nobuyuki Tsuchimura, 2014 .

A stronger multiple exchange property for $$\hbox {M}^{\natural }$$M♮-concave functions

K. Murota, 2017 .

A Stronger Multiple Exchange Property for M$^{\natural}$-concave Functions

K. Murota, 2017, 1706.09222.

Multiple Exchange Property for M$^\natural$-concave Functions and Valuated Matroids

K. Murota, 2016, 1608.07021.

On Some Properties of Polyhedral L-concave Maximization Algorithm

K. Murota, 2013 .

Submodular Function Minimization and Maximization in Discrete Convex Analysis (Combinatorial Optimization and Discrete Algorithms)

K. Murota, 2010 .

Note on Multimodularity and L-Convexity Kazuo MUROTA

K. Murota, 2004 .

Title Proximity Theorems of Discrete Convex Functions (Mathematics and Algorithms of Optimization)

K. Murota, A. Tamura, 2002 .

Fair Integral Submodular Flows

A. Frank, K. Murota, 2020, 2012.07325.

Self-organization of hexagonal agglomeration patterns in new economic geography models

K. Murota, T. Akamatsu, Yuki Takayama, 2014 .

Local Behavior Around Simple Critical Points

K. Murota, K. Ikeda, 2019, Imperfect Bifurcation in Structures and Materials.

Imperfection Sensitivity Laws

K. Murota, K. Ikeda, 2002 .

Stochastic Strength Variation at the Emergence of Parallel Shear Bands

K. Murota, S. Koyama, K. Ikeda, 1998 .

Worst Imperfection (I)

K. Murota, K. Ikeda, 2019, Imperfect Bifurcation in Structures and Materials.

Worst Imperfection (I)

K. Murota, K. Ikeda, 2010 .

Stable Economic Agglomeration Patterns in Two Dimensions: Beyond the Scope of Central Place Theory

K. Murota, Yuki Takayama, K. Ikeda, 2017 .

BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY

K. Murota, 2004 .

Rigorous proof of cubic convergence for the dqds algorithm for singular values

K. Murota, Takayasu Matsuo, Kensuke Aishima, 2008 .

MATHEMATICAL ENGINEERING TECHNICAL REPORTS Sperner's Lemma and the Existence of Zero on the Discrete Simplex and Simplotope

K. Murota, A. Tamura, Takuya Iimura, 2010 .

Imperfection Sensitivity Laws

K. Murota, K. Ikeda, 2019, Imperfect Bifurcation in Structures and Materials.

Fair Integral Network Flows

A. Frank, K. Murota, 2019, 1907.02673.

Self-Organization of LöSCH's Hexagons in Economic agglomeration for Core-periphery Models

Kazuo Murota, Kiyohiro Ikeda, Takashi Akamatsu, 2012, Int. J. Bifurc. Chaos.

Hexagonal distributions of cities in Southern Germany and Eastern USA: Group-theoretic spectrum analysis

K. Murota, Yuki Takayama, K. Ikeda, 2017 .

A Fast Parametric Submodular Intersection Algorithm for Strong Map Sequences

Satoru Iwata, Maiko Shigeno, Kazuo Murota, 1997, Math. Oper. Res..

Eigensets and power products of a bimatroid

K. Murota, 1990 .

9. Network Flows

Kazuo Murota, K. Murota, 2003 .

MATHEMATICAL ENGINEERING TECHNICAL REPORTS On Some Properties of Polyhedral L-concave

Kazuo Murota, Akiyoshi Shioura, K. Murota, 2013 .

6. M-Convex Functions

Kazuo Murota, K. Murota, 2003 .

Flower Patterns Appearing on a Honeycomb Structure and their bifurcation Mechanism

Kazuo Murota, Kiyohiro Ikeda, Isao Saiki, 2005, Int. J. Bifurc. Chaos.

Improvement of the scaled corrector method for bifurcation analysis using symmetry-exploiting block-diagonalization

K. Murota, K. Ikeda, H. Noguchi, 2007 .

MATHEMATICAL ENGINEERING TECHNICAL REPORTS Use of Primal-Dual Technique in the Network Algorithm for Two-Way Contingency Tables

Taiji Suzuki, Satoshi Aoki, Kazuo Murota, 2004 .

MATHEMATICAL ENGINEERING TECHNICAL REPORTS

Kazuo Murota, K. Murota, 2004 .

Electric Network Kernel for Support Vector Machines (Decision Theory and Optimization Algorithms)

Kazuo Murota, Masaki Rikitoku, Hiroshi Hirai, 2005 .

Computing Puiseux-Series Solutions to Determinantal Equations via Combinatorial Relaxation

Kazuo Murota, K. Murota, 1990, SIGAL International Symposium on Algorithms.

Numerical indefinite integration by double exponential sinc method

Kazuo Murota, Ken'ichiro Tanaka, Masaaki Sugihara, 2004, Math. Comput..

BENDERS DECOMPOSITION APPROACH TO ROBUST MIXED INTEGER PROGRAMMING

Kazuo Murota, K. Murota, Hiroo Saito, 2007 .

Fair integral submodular flows

A. Frank, K. Murota, 2020, Discret. Appl. Math..

Self-Organizing Hexagons in Economic Agglomeration: Core–Periphery Models and Central Place Theory

K. Murota, T. Akamatsu, Yuki Takayama, 2010 .

Use of primal-dual technique in the network algorithm for two-way contingency tables

Taiji Suzuki, K. Murota, S. Aoki, 2005 .

A Survey on Convergence Theorems of the dqds Algorithm for Computing Singular Values

K. Murota, Takayasu Matsuo, M. Sugihara, 2010 .

Two algorithms for valuated Δ-matroids

K. Murota, 1996 .

MATHEMATICAL ENGINEERING TECHNICAL REPORTS Simultaneous Singular Value Decomposition

K. Murota, Takanori Maehara, 2009 .

An Algorithm for Decomposition of Matrix *-Algebras Generated by Symmetric Matrices (Mathematical Programming in the 21st Century : Optimization Modeling and Algorithms)

M. Kojima, S. Kojima, K. Murota, 2009 .

Bifurcation of Steel Specimens

K. Murota, K. Ikeda, 2019, Imperfect Bifurcation in Structures and Materials.

Linear-Time Approximation Algorithms for Finding the Minimum-Weight Perfect Matching on a Plane

Kazuo Murota, Masao Iri, Shouichi Matsui, 1981, Inf. Process. Lett..

Hexagonal Distributions in Economic Geography and Krugman’s Core–Periphery Model

K. Murota, K. Ikeda, 2014 .

The Studentized Empirical Characteristic Function and Its Application to Test for the Shape of Distribution

K. Takeuchi, K. Murota, 1981, Contributions on Theory of Mathematical Statistics.

Time Bounds for Iterative Auctions with Multiple Differentiated Items : Discrete Convex Analysis Approach *

K. Murota, 2014 .

Group-Theoretic Bifurcation Theory

K. Murota, K. Ikeda, 2019, Imperfect Bifurcation in Structures and Materials.

Fair Integral Flows

A. Frank, K. Murota, 2019 .

2 Existing Two Formulations 2 . 1 Linear programming formulation

K. Murota, Kenjiro Takazawa, 2018 .

Continuous relaxation for discrete DC programming

K. Murota, Takanori Maehara, Naoki Marumo, 2017, Mathematical Programming.

Valuated matroid-based algorithm for submodular welfare problem

K. Murota, Takanori Maehara, 2015, Annals of Operations Research.

Cone superadditivity of discrete convex functions

K. Murota, R. Weismantel, Yusuke Kobayashi, 2011, Mathematical Programming.

Recent Progress on Integrally Convex Functions

K. Murota, A. Tamura, 2022, 2211.10912.

Inclusion and Intersection Relations Between Fundamental Classes of Discrete Convex Functions

K. Murota, Satoko Moriguchi, 2021, 2111.07240.

Scaling, proximity, and optimization of integrally convex functions

F. Tardella, K. Murota, A. Tamura, 2018, Mathematical Programming.

A framework of discrete DC programming by discrete convex analysis

K. Murota, Takanori Maehara, 2014, Mathematical Programming.

Dijkstra’s algorithm and L-concave function maximization

K. Murota, A. Shioura, 2013, Mathematical Programming.

Valuated matroid intersection, I: optimality criteria, II: algorithms

Kazuo Murota, K. Murota, 1996 .

Matroid Valuation on Independent Sets

Kazuo Murota, K. Murota, 1997, Journal of combinatorial theory. Series B (Print).

M-Convex Function on Generalized Polymatroid(Continuous and Discrete Mathematical Optimization)

K. Murota, A. Shioura, 1997 .

C O ] 5 J ul 2 01 9 Discrete Decreasing Minimization , Part III : Network Flows

A. Frank, K. Murota, 2019 .

A Discrete Convex Min-Max Formula for Box-TDI Polyhedra

András Frank, Kazuo Murota, A. Frank, 2020, Math. Oper. Res..

A systematic survey of the factors affecting zircaloy nodular corrosion

K. Murota, K. Ogata, Takuya Hattori, 1989 .

Discrete convex analysis

Kazuo Murota, K. Murota, 1998, Math. Program..

Electric Network Classifier for Semi-Supervised Learning on Graphs

Kazuo Murota, Hiroshi Hirai, Masaki Rikitoku, 2006 .

Voronoi Diagram in the Laguerre Geometry and its Applications

Hiroshi Imai, Kazuo Murota, Masao Iri, 1985, SIAM J. Comput..

Imperfect Bifurcation in Structures and Materials: Engineering Use of Group-Theoretic Bifurcation Theory. Applied Mathematical Sciences, Vol 149

Kazuo Murota, Kiyohiro Ikeda, K. Murota, 2002 .

Note on a graph-theoretic criterion for structural output controllability

Kazuo Murota, Svatopluk Poljak, S. Poljak, 1990 .

Decreasing minimization on base-polyhedra: relation between discrete and continuous cases

A. Frank, K. Murota, 2022, Japan Journal of Industrial and Applied Mathematics.

Continuous relaxation for discrete DC programming

Kazuo Murota, Takanori Maehara, Naoki Marumo, 2018, MCO.

A framework of discrete DC programming by discrete convex analysis

Kazuo Murota, Takanori Maehara, K. Murota, 2015, Math. Program..

Combinatorial dynamical system theory: General framework and controllability criteria

Kazuo Murota, K. Murota, 1989, Discret. Appl. Math..

A mathematical model for structural analysis of dynamical systems

K. Murota, 1990 .

Structural Controllability of a System with Some Fixed Coefficients

K. Murota, 1983 .

Bifurcation analysis of symmetric structures using block-diagonalization

Kazuo Murota, Kiyohiro Ikeda, K. Murota, 1991 .

Introduction to Economic Agglomeration on Hexagonal Lattice

K. Murota, K. Ikeda, 2014 .

Bifurcation mechanism underlying echelon-mode formation

K. Murota, K. Terada, K. Ikeda, 1999 .

Conjugacy relationship between M-convex and L-convex functions in continuous variables

Kazuo Murota, Akiyoshi Shioura, K. Murota, 2004, Math. Program..

Fundamental Properties of M-Convex and L-Convex Functions in Continuous Variables

Kazuo Murota, Akiyoshi Shioura, K. Murota, 2004 .

Deterministic network coding by matrix completion

David R. Karger, Kazuo Murota, Nicholas J. A. Harvey, 2005, SODA '05.

Algorithm for Error-Controlled Simultaneous Block-Diagonalization of Matrices

Kazuo Murota, Takanori Maehara, K. Murota, 2011, SIAM J. Matrix Anal. Appl..

Error-controlling algorithm for simultaneous block-diagonalization and its application to independent component analysis

Kazuo Murota, Takanori Maehara, K. Murota, 2010, JSIAM Lett..

A fast Voronoi-diagram algorithm with applications to geographical optimization problems

Kazuo Murota, Takao Ohya, Masao Iri, 1984 .

Function classes for double exponential integration formulas

Kazuo Murota, Ken'ichiro Tanaka, Masaaki Sugihara, 2009, Numerische Mathematik.

MATHEMATICAL ENGINEERING TECHNICAL REPORTS Function Classes for Double Exponential Integration Formulas

Kazuo Murota, Masatake Mori, Tanaka Masaaki Sugihara, 2007 .

A note on Haselgrove’s method for numerical integration

Kazuo Murota, Masaaki Sugihara, K. Murota, 1982 .

Parameter tuning and repeated application of the IMT-type transformation in numerical quadrature

M. Iri, K. Murota, 1980 .

Menger-decomposition of a graph and its application to the structural analysis of a large-scale system of equations

Kazuo Murota, K. Murota, 1982, Discret. Appl. Math..

Cone superadditivity of discrete convex functions

Kazuo Murota, Yusuke Kobayashi, Robert Weismantel, 2012, Math. Program..

Asymptotic and Probabilistic Approach to Buckling of Structures and Materials

Kazuo Murota, Kiyohiro Ikeda, K. Murota, 2008 .

Time bounds for iterative auctions: A unified approach by discrete convex analysis

Kazuo Murota, Akiyoshi Shioura, Zaifu Yang, 2016, Discret. Optim..

Computing a Walrasian Equilibrium in Iterative Auctions with Multiple Differentiated Items

Zaifu Yang, Kazuo Murota, Akiyoshi Shioura, 2013, ISAAC.

Discrete convexity and equilibria in economies with indivisible goods and money

Kazuo Murota, Gleb A. Koshevoy, Vladimir I. Danilov, 2001, Math. Soc. Sci..

Decreasing minimization on M-convex sets: algorithms and applications

Kazuo Murota, Andr'as Frank, A. Frank, 2020, Mathematical Programming.

Discrete Decreasing Minimization, Part I: Base-polyhedra with Applications in Network Optimization

Kazuo Murota, Andr'as Frank, A. Frank, 2018, 1808.07600.

Valuated Matroid Intersection I: Optimality Criteria

Kazuo Murota, K. Murota, 1996, SIAM J. Discret. Math..

Convexity and Steinitz's Exchange Property

Kazuo Murota, K. Murota, 1996, IPCO.

Algorithms in discrete convex analysis

Kazuo Murota, K. Murota, 2000 .

On the Degree of Mixed Polynomial Matrices

Kazuo Murota, K. Murota, 1998, SIAM J. Matrix Anal. Appl..

Dijkstra’s algorithm and L-concave function maximization

Kazuo Murota, Akiyoshi Shioura, K. Murota, 2014, Math. Program..

MATHEMATICAL ENGINEERING TECHNICAL REPORTS Recent Developments in Discrete Convex Analysis

Kazuo Murota, K. Murota, 2008 .

IMPROVEMENTS OF THE INCREMENTAL METHOD FOR THE VORONOI DIAGRAM WITH COMPUTATIONAL COMPARISON OF VARIOUS ALGORITHMS

Kazuo Murota, Takao Ohya, Masao Iri, 1984 .

An identity for matching and skew-symmetric determinant☆

Kazuo Murota, K. Murota, 1995 .

Present status and future direction of light water reactor fuel fabrication, quality assurance in nuclear fuel manufacture.

Kazuo Murota, K. Murota, 1987 .

Computing Puiseux-Series Solutions to Determinantal Equations via Combinatorial Relaxation

Kazuo Murota, K. Murota, 1990, SIAM J. Comput..

A shift strategy for superquadratic convergence in the dqds algorithm for singular values

Kazuo Murota, Masaaki Sugihara, Takayasu Matsuo, 2014, J. Comput. Appl. Math..

Superquadratic convergence of DLASQ for computing matrix singular values

Kazuo Murota, Masaaki Sugihara, Takayasu Matsuo, 2010, J. Comput. Appl. Math..

On Convergence of the DQDS Algorithm for Singular Value Computation

Kazuo Murota, Masaaki Sugihara, Takayasu Matsuo, 2008, SIAM J. Matrix Anal. Appl..

Uncertainty in the strength of materials and structures

Kiyohiro Ikeda, Kazuo Murota, K. Maruyama, 1998 .

Group-theoretic spectrum analysis of hexagonal city distributions in Southern Germany and Eastern USA

K. Murota, Yuki Takayama, K. Ikeda, 2016 .

Imperfection Sensitivity Laws

K. Murota, K. Ikeda, 2019, Imperfect Bifurcation in Structures and Materials.

The linear delta-matroid parity problem

Satoru Iwata, Kazuo Murota, James F. Geelen, 2003, J. Comb. Theory, Ser. B.

Quasi M-convex and L-convex functions--quasiconvexity in discrete optimization

Kazuo Murota, Akiyoshi Shioura, K. Murota, 2003, Discret. Appl. Math..

Notes on L-/M-convex functions and the separation theorems

Kazuo Murota, Satoru Fujishige, S. Fujishige, 2000, Math. Program..

MATHEMATICAL ENGINEERING TECHNICAL REPORTS A Note on "Order-Based Cost Optimization in Assemble-to-Order Systems"

Kazuo Murota, Woonghee Tim Huh, W. T. Huh, 2015 .

Proximity theorems of discrete convex functions

Kazuo Murota, Akihisa Tamura, K. Murota, 2004, Math. Program..

Scaling Algorithms for M-Convex Function Minimization

Kazuo Murota, Satoko Moriguchi, Akiyoshi Shioura, 2002, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

M-Convex Function on Generalized Polymatroid

Kazuo Murota, Akiyoshi Shioura, K. Murota, 1999, Math. Oper. Res..

MATHEMATICAL ENGINEERING TECHNICAL REPORTS Recent Developments in Discrete Convex Analysis

Kazuo Murota, K. Murota, 2008 .

Extension of M-Convexity and L-Convexity to Polyhedral Convex Functions

Kazuo Murota, Akiyoshi Shioura, K. Murota, 1999, Adv. Appl. Math..

ON FUNDAMENTAL OPERATIONS FOR MULTIMODULAR FUNCTIONS

Kazuo Murota, Satoko Moriguchi, K. Murota, 2018, Journal of the Operations Research Society of Japan.

Note on Multimodularity and L-Convexity

Kazuo Murota, K. Murota, 2005, Math. Oper. Res..

On Steepest Descent Algorithms for Discrete Convex Functions

Kazuo Murota, K. Murota, 2003, SIAM J. Optim..

Decreasing minimization on M-convex sets: background and structures

Kazuo Murota, Andr'as Frank, K. Murota, 2020, Mathematical Programming.

Horizontal Principal Structure of Layered Mixed Matrices: Decomposition of Discrete Systems by Design-Variable Selections

Satoru Iwata, Kazuo Murota, K. Murota, 1996, SIAM J. Discret. Math..

A Theorem on the Principal Structure for Independent Matchings

Satoru Iwata, Kazuo Murota, K. Murota, 1995, Discret. Appl. Math..

Principal structure of layered mixed matrices

Kazuo Murota, K. Murota, 1990, Discret. Appl. Math..

Combinatorial canonical form of layered mixed matrices and its application to block-triangularization of systems of linear/nonlinear equations

Kazuo Murota, Masao Iri, M. Iri, 1987 .

Flower Patterns on Honeycomb Structures

K. Murota, K. Ikeda, 2019, Imperfect Bifurcation in Structures and Materials.

Hexagonal Distributions on Hexagonal Lattice

K. Murota, K. Ikeda, 2014 .

Echelon-Mode Formation

K. Murota, K. Ikeda, 2002 .

A numerical algorithm for block-diagonal decomposition of matrix $${*}$$-algebras with application to semidefinite programming

Yoshihiro Kanno, Kazuo Murota, Masakazu Kojima, 2010 .

Decomposition of an Integrally Convex Set into a Minkowski Sum of Bounded and Conic Integrally Convex Sets

K. Murota, A. Tamura, 2023, 2306.09072.

Recent progress on integrally convex functions

K. Murota, A. Tamura, 2022, Japan Journal of Industrial and Applied Mathematics.

INCLUSION AND INTERSECTION RELATIONS BETWEEN FUNDAMENTAL CLASSES OF DISCRETE CONVEX FUNCTIONS

K. Murota, Satoko Moriguchi, 2021, Journal of the Operations Research Society of Japan.

Note on the polyhedral description of the Minkowski sum of two L-convex sets

K. Murota, Satoko Moriguchi, 2021, Japan Journal of Industrial and Applied Mathematics.

Discrete Fenchel duality for a pair of integrally convex and separable convex functions

Kazuo Murota, Akihisa Tamura, K. Murota, 2021, Japan Journal of Industrial and Applied Mathematics.

Integrality of subgradients and biconjugates of integrally convex functions

K. Murota, A. Tamura, 2019, Optimization Letters.

Integrality of subgradients and biconjugates of integrally convex functions

Kazuo Murota, Akihisa Tamura, K. Murota, 2018, Optim. Lett..

Scaling, proximity, and optimization of integrally convex functions

Fabio Tardella, Kazuo Murota, Akihisa Tamura, 2017, Math. Program..

Combinatorial relaxation algorithm for the maximum degree of subdeterminants: Computing Smith-Mcmillan form at infinity and structural indices in Kronecker form

Kazuo Murota, K. Murota, 1995, Applicable Algebra in Engineering, Communication and Computing.

Hexagons of Christaller and Lösch: Using Equivariant Branching Lemma

K. Murota, K. Ikeda, 2014 .

On basic operations related to network induction of discrete convex functions

K. Murota, 2020, Optim. Methods Softw..

Simpler exchange axioms for M-concave functions on generalized polymatroids

Kazuo Murota, Akiyoshi Shioura, K. Murota, 2018 .

Quadratic M-convex and L-convex functions

Kazuo Murota, Akiyoshi Shioura, K. Murota, 2004, Adv. Appl. Math..

MATHEMATICAL ENGINEERING TECHNICAL REPORTS On the Number of Matrices to Generate a Matrix ∗-Algebra over the Real Field

Naonori Kakimura, Daishi Aiura, Kazuo Murota, 2013 .

Discrete Decreasing Minimization, Part I: Base-polyhedra with Applications in Network Optimization

A. Frank, K. Murota, 2018, 1808.07600.

On Equivalence of M$^\natural$-concavity of a Set Function and Submodularity of Its Conjugate

K. Murota, A. Shioura, 2017, 1707.09091.

Valuated matroid-based algorithm for submodular welfare problem

Kazuo Murota, Takanori Maehara, K. Murota, 2015, Ann. Oper. Res..

Induction of M-convex functions by linking systems

Kazuo Murota, Yusuke Kobayashi, K. Murota, 2007, Discret. Appl. Math..

Operations on M-Convex Functions on Jump Systems

Kazuo Murota, Yusuke Kobayashi, Ken'ichiro Tanaka, 2007, SIAM J. Discret. Math..

Substitutes and complements in network flows viewed as discrete convexity

Kazuo Murota, Akiyoshi Shioura, K. Murota, 2005, Discret. Optim..

Discrete Hessian Matrix for L-Convex Functions

Kazuo Murota, Satoko Moriguchi, K. Murota, 2005, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

A capacity scaling algorithm for M-convex submodular flow

Satoru Iwata, Kazuo Murota, Satoko Moriguchi, 2004, Math. Program..

A Proof of the M-Convex Intersection Theorem (Applications of Discrete Convex Analysis to Game Theory and Mathematical Economics)

K. Murota, 2004 .

Capacity scaling algorithm for scalable M-convex submodular flow problems

Kazuo Murota, Satoko Moriguchi, K. Murota, 2003, Optim. Methods Softw..

Relationship of M-/L-convex functions with discrete convex functions by Miller and Favati-Tardella

Kazuo Murota, Akiyoshi Shioura, K. Murota, 2001, Discret. Appl. Math..

Valuated Matroid Intersection II: Algorithms

Kazuo Murota, K. Murota, 1996, SIAM J. Discret. Math..

A stronger multiple exchange property for M (cid:2) -concave functions

K. Murota, 2017 .

M-Convex Functions on Jump Systems: A General Framework for Minsquare Graph Factor Problem

Kazuo Murota, K. Murota, 2006, SIAM J. Discret. Math..

Optimality criterion for a class of nonlinear integer programs

Kazuo Murota, Hiroo Saito, Robert Weismantel, 2004, Oper. Res. Lett..

Exchange Properties of M-natural-concave Set Functions and Valuated Matroids

K. Murota, 2021, 2105.14228.

Disturbance Decoupling with Pole Placement for Structured Systems: A Graph-Theoretic Approach

Kazuo Murota, Jacob van der Woude, K. Murota, 1995, SIAM J. Matrix Anal. Appl..

Systems Analysis by Graphs and Matroids

Kazuo Murota, K. Murota, 1987 .

Recursive Bifurcation as Sources of Complexity in Soil Shearing Behavior

Kazuo Murota, Kiyohiro Ikeda, K. Murota, 1997 .

An identity for bipartite matching and symmetric determinant

Kazuo Murota, K. Murota, 1995 .

On Circuit Valuation of Matroids

Kazuo Murota, Akihisa Tamura, K. Murota, 2001, Adv. Appl. Math..

Legendre duality in combinatorial study of matrix pencils

K. Murota, 2011, Japan Journal of Industrial and Applied Mathematics.

Hierarchical decomposition of symmetric discrete systems by matroid and group theories

Kazuo Murota, K. Murota, 1993, Math. Program..

MATHEMATICAL ENGINEERING TECHNICAL REPORTS Legendre Duality in Combinatorial Study of Matrix Pencils

K. Murota, 2011 .

Mixed Matrices — Irreducibility and Decomposition — ⁄

Kazuo Murota, K. Murota, 1993 .

Matroidal Approach to the Structural Solvability of a System of Equations

M. Iri, K. Murota, 1983 .

Application of Semidefinite Programming to Maximize the Spectral Gap Produced by Node Removal

Kazuo Murota, Naoki Masuda, Tetsuya Fujie, 2013, CompleNet.

Application of M-Convex submodular flow problem to mathematical economics

Kazuo Murota, Akihisa Tamura, K. Murota, 2001, ISAAC.

On the Lattice Structure of Stable Allocations in a Two-Sided Discrete-Concave Market

Kazuo Murota, Yu Yokoi, K. Murota, 2015, Math. Oper. Res..

MATHEMATICAL ENGINEERING TECHNICAL REPORTS Valuated Matroid-Based Algorithm for Submodular Welfare Problem

K. Murota, Takanori Maehara, 2013 .

Continuous relaxation for discrete DC programming

Kazuo Murota, Takanori Maehara, Naoki Marumo, 2017, Mathematical programming.

MATHEMATICAL ENGINEERING TECHNICAL REPORTS A Framework of Discrete DC Programming by Discrete Convex Analysis

K. Murota, Takanori Maehara, 2013 .

ON DISCRETE HESSIAN MATRIX AND CONVEX EXTENSIBILITY

Kazuo Murota, Satoko Moriguchi, K. Murota, 2012 .

On the Smith normal form of structured polynomial matrices

Kazuo Murota, K. Murota, 1991 .

A matroid-theoretic approach to structurally fixed modes of control systems

Kazuo Murota, K. Murota, 1989 .

On the irreducibility of layered mixed matrices

Kazuo Murota, K. Murota, 1989 .

Agglomeration patterns in a long narrow economy of a new economic geography model: Analogy to a racetrack economy

K. Murota, T. Akamatsu, Yuki Takayama, 2017 .

Agglomeration in Racetrack Economy

K. Murota, K. Ikeda, 2014 .

MATHEMATICAL ENGINEERING TECHNICAL REPORTS Self-Organization of L ¨ osch's Hexagons in Economic Agglomeration for Core-Periphery Models

Kazuo Murota, Kiyohiro Ikeda, Takashi Akamatsu, 2011 .

for Core-Periphery Models: Central Place Theory and Group Theory

K. Murota, T. Akamatsu, Yuki Takayama, 2011 .

Combinatorial relaxation algorithm for mixed polynomial matrices

Satoru Iwata, Kazuo Murota, K. Murota, 2001, Math. Program..

Primal-Dual Combinatorial Relaxation Algorithms for the Maximum Degree of Subdeterminants

Satoru Iwata, Kazuo Murota, Izumi Sakuta, 1996, SIAM J. Sci. Comput..

Computing the Degree of Determinants Via Combinatorial Relaxation

Kazuo Murota, K. Murota, 1995, SIAM J. Comput..

MATHEMATICAL ENGINEERING TECHNICAL REPORTS A Survey on Convergence Theorems of the dqds Algorithm for Computing Singular Values

K. Murota, Takayasu Matsuo, M. Sugihara, 2009 .

Linear Programming

K. Murota, 2020, Computer Vision.

Shapley-Folkman-type Theorem for Integrally Convex Sets

K. Murota, A. Tamura, 2023, 2305.15125.

Double-Exponential transformation: A quick review of a Japanese tradition

K. Murota, Takayasu Matsuo, 2023, ArXiv.

Computational Use of Group Theory in Bifurcation Analysis of Symmetric Structures

Kazuo Murota, Kiyohiro Ikeda, K. Murota, 1991, SIAM J. Sci. Comput..

Bifurcation Behavior of Dn-Equivariant Systems

K. Murota, K. Ikeda, 2019, Imperfect Bifurcation in Structures and Materials.

Bifurcation Behavior of D n -Equivariant Systems

K. Murota, K. Ikeda, 2002 .

A Wilkinson-like multishift QR algorithm for symmetric eigenvalue problems and its global convergence

Kazuo Murota, Masaaki Sugihara, Takayasu Matsuo, 2012, J. Comput. Appl. Math..

Bifurcations to diversify geometrical patterns of shear bands on granular material.

K. Murota, Y. Yamakawa, K. Ikeda, 2008, Physical review letters.

Bifurcation Behaviors of Cylindrical Soils

K. Murota, K. Ikeda, 2019, Imperfect Bifurcation in Structures and Materials.

Mode switching and recursive bifurcation in granular materials

Kazuo Murota, Yuki Yamakawa, Kiyohiro Ikeda, 1997 .

Echelon modes in uniform materials

K. Murota, K. Ikeda, M. Nakano, 1994 .