教員紹介

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教員情報

教員名室田　一雄教員名カナムロタ　カズオ

英字
所属経済経営学部経済経営学科

詳細情報

学部・コース等

研究科・専攻等特別先導教授として，研究に従事した．
・離散凸解析の理論と応用に関して，整凸関数を中心に研究を行った．
・原著論文を数編，執筆し，プレプリントの形でarXiv等に公開した．
・離散凸解析の集大成に向けて，図書の執筆に取り組んだ．

職位特別先導教授

専攻分野数理工学，オペレーションズ・リサーチ，最適化

最終学歴・学位東京大学大学院工学系研究科計数工学専攻修士課程修了
工学博士（東京大学），博士（理学，京都大学）

研究テーマ離散凸解析，最適化の理論と応用，マトロイド理論のシステム解析への応用，群論的分岐理論の構造工学への応用，数値計算法など，数理工学の研究を幅広く行っている．

研究キーワード離散凸解析，グラフ，マトロイド，アルゴリズム，数理モデリング

研究業績・著者・論文、その他それに準じる業績 ●著書

K. Murota (1987): Systems Analysis by Graphs and Matroids, Springer.
K. Murota (2000): Matrices and Matroids for Systems Analysis. Springer.

K. Murota (2003): Discrete Convex Analysis, SIAM.
室田一雄 (2001): 離散凸解析. 共立出版.
室田一雄 (2007): 離散凸解析の考えかた，共立出版.
室田一雄，塩浦昭義 (2013): 離散凸解析と最適化アルゴリズム，朝倉書店.

室田一雄，杉原正顯 (2015): 線形代数I，東京大学工学教程（基礎系数学），丸善出版.
室田一雄，杉原正顯 (2013): 線形代数II，東京大学工学教程（基礎系数学），丸善出版.
K. Murota and M. Sugihara (2022): Linear Algebra I: Basic Concepts, UTokyo Engineering Course/Basic Mathematics, World Scientific and Maruzen Publishing.
K. Murota and M. Sugihara (2022): Linear Algebra II: Advanced Topics for Applications, UTokyo Engineering Course/Basic Mathematics, World Scientific and Maruzen Publishing.

杉原正顯, 室田一雄 (1994): 数値計算法の数理, 岩波書店.
杉原正顯, 室田一雄 (2009): 線形計算の数理, 岩波書店.

K. Ikeda and K. Murota (2002): Imperfect Bifurcation in Structures and Materials
--- Engineering Use of Group-Theoretic Bifurcation Theory, Springer.
K. Ikeda and K. Murota (2010): Imperfect Bifurcation in Structures and Materials
--- Engineering Use of Group-Theoretic Bifurcation Theory, Second Edition, Springer.
K. Ikeda and K. Murota (2019): Imperfect Bifurcation in Structures and Materials
--- Engineering Use of Group-Theoretic Bifurcation Theory,Third Edition, Springer.

池田清宏，室田一雄 (2001): 構造系の座屈と分岐, コロナ社.
K. Ikeda and K. Murota (2022): Bifurcation and Buckling in Structures, CRC Press.

K. Ikeda and K. Murota (2014): Bifurcation Theory for Hexagonal Agglomeration in Economic Geography, Springer

青本和彦, 上野健爾, 加藤和也, 神保道夫, 砂田利一, 高橋陽一郎, 深谷賢治, 俣野博, 室田一雄編著(2005)：数学入門辞典，岩波書店.

など

●論文(離散凸解析に関する論文)

K. Murota (1996): Valuated matroid intersection, I: optimality criteria, SIAM Journal on Discrete Mathematics, Vol.9,　pp.545-561.

K. Murota (1996): Valuated matroid intersection, II: algorithms, SIAM Journal on Discrete Mathematics, Vol.9, pp.562-576.

K. Murota (1996): Convexity and Steinitz's exchange property, Advances in Mathematics, Vol.124, pp.272-311.

K. Murota (1998): Fenchel-type duality for matroid valuations, Mathematical Programming, Vol.82, pp. 357--375.

K. Murota (1998): Discrete convex analysis, Mathematical Programming, Vol.83, pp.313-371.

K. Murota (1999): Submodular flow problem with a nonseparable cost function, Combinatorica, Vol.19, pp.87-109.

K. Murota and A. Shioura (1999): M-Convex function on generalized polymatroid, Mathematics of Operations Research, Vol.24, pp.95-105.

S. Fujishige and K. Murota (2000): Notes on L-/M-convex functions and the separation theorems, Mathematical Programming, Vol. 88, pp.129-146.

K. Murota and A. Shioura (2000): Extension of M-convexity and L-convexity to polyhedral convex functions, Advances in Applied Mathematics, Vol. 25, pp.352-427.

V. Danilov, G. Koshevoy, and K. Murota (2001): Discrete convexity and equilibria in economies with indivisible
goods and money, Mathematical Social Sciences, Vol.41, pp.251-273.

S. Moriguchi, K. Murota and A. Shioura (2002): Scaling algorithms for M-convex function minimization, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E85-A, pp.922-929.

S. Moriguchi and K. Murota (2003): Capacity scaling algorithm for scalable M-convex submodular flow problems, Optimization Methods and Software, Vol.18, pp.207--218.

K. Murota (2003): On steepest descent algorithms for discrete convex functions, SIAM Journal on Optimization, Vol.14, pp.699-707.

K. Murota and A. Tamura (2003): New characterizations of M-convex functions and their applications to economic equilibrium models with indivisibilities, Discrete Applied Mathematics, Vol.131, pp.495-512.

K. Murota and A. Tamura (2003):Application of M-convex submodular flow problem to mathematical economics, Japan Journal of Industrial and Applied Mathematics, Vol. 20, pp.257--277.

K. Murota and A. Shioura (2003): Quasi M-convex and L-convex functions---Quasi-convexity in discrete optimization, Discrete Applied Mathematics, Vol.~131/132, pp.467-494.

H. Hirai and K. Murota (2004): M-convex functions and tree metrics, Japan Journal of Industrial and Applied Mathematics, Vol. 21, pp.391-403.

K. Murota and A. Shioura (2004): Conjugacy relationship between M-convex and L-convex functions in continuous variables, Mathematical Programming, Vol.A101, pp.415-433.

K. Murota and A. Shioura (2004): Quadratic M-convex and L-convex functions, Advances in Applied Mathematics, Vol.33, pp.318-341.

K. Murota and A. Tamura (2004):Proximity theorems of discrete convex functions, Mathematical Programming, Vol.A99, pp.539-562.

T. Iimura, K. Murota, and A. Tamura (2005): Discrete fixed point theorem recon-sidered, Journal of Mathematical Economics, Vol.41, pp.1030-1036.

S. Iwata, S. Moriguchi and K. Murota (2005): A capacity scaling algorithm for M-convex submodular flow, Mathematical Programming, Vol.103, pp.181-202.

S. Moriguchi and K. Murota (2005): Discrete Hessian matrix for L-convex functions, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E88-A, pp.1104-1108.

K. Murota (2005): Note on multimodularity and L-convexity, Mathematics of Operations Research, Vol. 30, pp.658-661.

K. Murota and A. Shioura (2005): Substitutes and complements in network flows viewed as discrete convexity, Discrete Optimization, Vol. 2, pp.256-268.

K. Murota (2006): M-convex functions on jump systems: A general framework for minsquare graph factor problem, SIAM Journal on Discrete Mathematics, Vol. 20, pp.213-226.

Y. Kobayashi, K. Murota and K. Tanaka (2007): Operations on M-convex functions on jump systems, SIAM Journal on Discrete Mathematics, Vol. 21, pp.107-129.

Y. Kobayashi and K. Murota (2007): Induction of M-convex functions by linking systems, Discrete Applied Mathematics, Vol.155, pp.1471-1480.

K. Murota and A. Shioura (2008): Note on the continuity of M-convex and L-convex functions in continuous variables, Journal of the Operations Research Society of Japan, Vol.51, pp.265-273.

K. Murota (2009): Recent developments in discrete convex analysis, in: W. Cook, L. Lovasz and J. Vygen, eds., Research Trends in Combinatorial Optimization, Bonn 2008 , Springer, Chapter 11, pp.219-260.

K. Murota (2010): Submodular function minimization and maximization in discrete convex analysis, RIMS Kokyuroku Bessatsu, Vol.B23, pp.193-211.

Y. Kobayashi, K. Murota and R. Weismantel (2012): Cone superadditivity of discrete convex functions, Mathematical Programming, Series A, Vol. 135, pp.25-44.

S. Moriguchi and K. Murota (2012): On discrete Hessian matrix and convex extensibility, Journal of the Operations Research Society of Japan, Vol. 55, pp.48-62.

K. Murota and A. Shioura (2014): Dijkstra's algorithm and L-concave function maximization, Mathematical Programming, Series A, Vol.145, pp.163-177.

K. Murota and A. Shioura (2014): Exact bounds for steepest descent algorithms of L-convex function minimization, Operations Research Letters, Vol.42, pp.361-366.

T. Maehara and K. Murota (2015): A framework of discrete DC programming by discrete convex analysis, Mathematical Programming, Series A, Vol.152, pp.435-466.

T. Maehara and K. Murota (2015): Valuated matroid-based algorithm for submodular welfare problem, Annals of Operations Research, Vol.229, pp.565-590.

S. Fujishige, K. Murota and A. Shioura (2015): Monotonicity in steepest ascent algorithms for polyhedral L-concave functions, Journal of the Operations Research Society of Japan, Vol.58, pp.184-208.

K. Murota (2015): On polyhedral approximation of L-convex and M-convex functions, Journal of the Operations Research Society of Japan, Vol. 58, pp.291-305.

K. Murota, and Y. Yokoi (2015): On the lattice structure of stable allocations in two-sided discrete-concave market, Mathematics of Operations Research, Vol. 40, pp.460-473.

K. Murota, A. Shioura and Z. Yang (2016): Time bounds for iterative auctions: A unified approach by discrete convex analysis, Discrete Optimization, Vol.19, pp.36-62.

K. Murota (2016): Discrete convex analysis: A tool for economics and game theory, Journal of Mechanism and Institution Design, Vol.1, No.1, pp.151-273.

K. Murota and A. Shioura (2017): Note on time bounds of two-phase algorithms for L-convex function minimization, Japan Journal of Industrial and Applied Mathematics, Vol. 34, pp.429-440.

K. Murota (2018): A stronger multiple exchange property for M#-concave functions, Japan Journal of Industrial and Applied Mathematics, Vol.35, No.1, pp. 411-421.

K. Murota and A. Shioura (2018): On equivalence of M#-concavity of a set function and submodularity of its conjugate, Journal of the Operations Research Society of Japan, Vol.61, No.2, pp.163-171.

K. Murota and A. Shioura (2018): Simpler exchange axioms for M-concave functions on generalized polymatroids,
Japan Journal of Industrial and Applied Mathematics, Vol.35 , No.1, pp.235-259.

T. Maehara, N. Marumo, and K. Murota (2018): Continuous relaxation for discrete DC programming, Mathematical Programming, Series B, Vol.169, pp. 199-219 .

K. Murota (2018): Multiple exchange property for M#-concave functions and valuated matroids, Mathematics of Operations Research, Vol. 43, No. 3, pp. 781-788.

Y. Iwamasa, K. Murota, and S. Zivny (2018): Discrete convexity in joint winner property, Discrete Optimization, Vol.28, pp.78-88.

S. Moriguchi, K. Murota, A. Tamura, and F. Tardella (2019): Scaling, proximity, and optimization of integrally convex functions, Mathematical Programming, Vol.175, pp.119-154.

M. Bolandnazar, W. T. Huh, S. T. McCormick, and K. Murota (2019): Error noted in ``Order-Based Cost Optimization in Assemble-to-Order Systems'' by Lu and Song (2005), Operations Research, Vol. 67, pp.163-166.

S. Moriguchi and K. Murota (2019): Projection and convolution operations for integrally convex functions, Discrete Applied Mathematics, Vol.255, pp.283-298.

S. Moriguchi and K. Murota (2019): On fundamental operations for multimodular functions, Journal of the Operations Research Society of Japan, Vol.62, pp.53-63.

H. Hirai, Y. Iwamasa, K. Murota, and S.Zivny (2019): A tractable class of binary VCSPs via M-convex intersection,
ACM Transactions on Algorithms, Vol.15, No.3, Article 44 (July 2019), 41 pages. Online: https://doi.org/10.1145/3329862

S. Moriguchi, K. Murota, A. Tamura, and F. Tardella (2020): Discrete midpoint convexity, Mathematics of Operations Research,Vol. 45, pp.99-128.

K. Murota and A. Tamura (2020): Integrality of subgradients and biconjugates of integrally convex functions, Optimization Letters, Vol.14, pp.195-208.

K. Murota and K. Takazawa (2021): Relationship of two formulations for shortest bibranchings, Japan Journal of Industrial and Applied Mathematics, Vol.38, No.1, pp.141-161.

K. Murota (2021): A survey of fundamental operations on discrete convex functions of various kinds, Optimization Methods and Software, Vol.36 , Nos.2-3, pp.472-518.

K. Murota (2021): On basic operations related to network induction of discrete convex functions, Optimization Methods and Software, Vol.36, Nos.2-3, pp.519-559.

K. Murota (2021): A note on M-convex functions on jump systems, Discrete Applied Mathematics, Vol.289, pp.492--502.

A. Frank and K. Murota (2022): A discrete convex min-max formula for box-TDI polyhedra, Mathematics of Operations Research, Vol.47, No.2, pp.1026-1047. https://doi.org/10.1287/moor.2021.1160.

A. Frank and K. Murota (2022): Decreasing minimization on M-convex sets: Background and Structures, Mathematical Programming, Vol.195, No.1-2, pp.977-1025. https://doi.org/10.1007/s10107-021-01722-2

A. Frank and K. Murota (2022): Decreasing minimization on M-convex sets: Algorithms and applications, Mathematical Programming, Vol.195 , No.1-2, pp.1027-1068. https://doi.org/10.1007/s10107-021-01711-5

K. Murota and A. Tamura (2022): Discrete Fenchel duality for a pair of integrally convex and separable convex functions, Japan Journal of Industrial and Applied Mathematics, Vol.39, No.2, pp.599-630.

A. Frank and K. Murota (2022): Fair integral submodular flows, Discrete Applied Mathematics, Vol.320, pp.416-434.

A. Frank and K. Murota (2023): Fair integral network flows, Mathematics of Operations Research, Vol.48, No.3, pp. 1393-1422.

A. Frank and K. Murota (2023): Decreasing minimization on base-polyhedra: Relation between discrete and continuous cases, Japan Journal of Industrial and Applied Mathematics, Vol.40, No.1, pp.183-221.

S. Moriguchi and K. Murota (2023): Note on the polyhedral description of the Minkowski sum of two L-convex sets, Japan Journal of Industrial and Applied Mathematics, Vol.40, No.1, pp.223-263. https://doi.org/10.1007/s13160-022-00512-3 (Open access).

S. Moriguchi and K. Murota (2023): Inclusion and intersection relations between fundamental classes of discrete convex functions, Journal of the Operations Research Society of Japan, Vol. 66, No.3, pp.187-217.

K. Murota and A. Tamura (2023): Recent progress on integrally convex functions, Japan Journal of Industrial and Applied Mathematics, Vol.40, No.3, pp.1445-1499. https://doi.org/10.1007/s13160-023-00589-4 (Open access)

K. Murota and A. Shioura (2024): Note on minimization of quasi M-natural-convex functions, Japan Journal of Industrial and Applied Mathematics, Vol.41 (2024), No.2, ***--***. https://doi.org/10.1007/s13160-023-00633-3 (Open access)

K. Murota and A. Tamura (2024): Decomposition of an integrally convex set into a Minkowski sum of bounded and conic integrally convex sets, Japan Journal of Industrial and Applied Mathematics, Vol.41 (2024), No.2, ***--***. https://doi.org/10.1007/s13160-023-00635-1 (Open access)

など

●論文(初期の論文)

K. Murota and K. Takeuchi (1981): The studentized empirical characteristic function and its application to test for the shape of distribution, Biometrika, Vol.68, pp.55-65. Included in: K. Takeuchi: Contributions on Theory of Mathematical Statistics, Springer, 2020, Chapter 9, pp.221-235.

K. Murota and M. Iri (1982): Parameter tuning and repeated application of the IMT-type transformation in numerical quadrature, Numerische Mathematik, Vol.38, pp.347-363.

K. Murota (1982): Global convergence of a modified Newton iteration for algebraic equations, SIAM Journal on Numerical Analysis, Vol.19, pp.793-799.

M. Iri, K. Murota and S. Matsui (1983): Heuristics for planar minimum-weight perfect matchings, Networks, Vol.13, pp.67-92.

T. Ohya, M. Iri and K. Murota (1984): Improvements of the incremental method for the Voronoi diagram with computational comparison of various algorithms, Journal of the Operations Research Society of Japan, Vol.27, pp.306-337.

K. Murota and M. Iri (1985): Structural solvability of systems of equations---A mathematical formulation for distinguishing accurate and inaccurate numbers in structural analysis of systems, Japan Journal of Applied Mathematics, Vol.2, pp.247-271.

K. Murota (1985): Use of the concept of physical dimensions in the structural approach to systems analysis, Japan Journal of Applied Mathematics, Vol.2, pp.471-494.

●詳細は　
http://www.comp.tmu.ac.jp/kzmurota/publist.html

受賞第２回　日本IBM科学賞（1988年）
日本オペレーションズ・リサーチ学会文献賞（1994年）
第２１回　井上学術賞（2004年）
日本オペレーションズ・リサーチ学会業績賞（2014年）
日本応用数理学会業績賞 (2019年)
日本オペレーションズ・リサーチ学会近藤賞（2021年）
など

主な学会活動日本応用数理学会，フェロー
日本オペレーションズ・リサーチ学会フェロー，副会長 (2014-2015)

社会等との関わり

個人のURL http://kzmurota.fpark.tmu.ac.jp/

担当科目

オフィスアワー

研究室

内線番号

メールアドレス murota●tmu.ac.jp
（メールを送信する場合は●を@に変換してください）

研究室サイト等 http://kzmurota.fpark.tmu.ac.jp/

取組状況令和05年度

researchmap 過去の研究業績等(researchmap)

教員情報
教員名	室田　一雄	教員名カナ	ムロタ　カズオ
英字		所属	経済経営学部経済経営学科

詳細情報
学部・コース等
研究科・専攻等	特別先導教授として，研究に従事した．・離散凸解析の理論と応用に関して，整凸関数を中心に研究を行った．・原著論文を数編，執筆し，プレプリントの形でarXiv等に公開した．・離散凸解析の集大成に向けて，図書の執筆に取り組んだ．
職位	特別先導教授
専攻分野	数理工学，オペレーションズ・リサーチ，最適化
最終学歴・学位	東京大学大学院工学系研究科計数工学専攻修士課程修了工学博士（東京大学），博士（理学，京都大学）
研究テーマ	離散凸解析，最適化の理論と応用，マトロイド理論のシステム解析への応用，群論的分岐理論の構造工学への応用，数値計算法など，数理工学の研究を幅広く行っている．
研究キーワード	離散凸解析，グラフ，マトロイド，アルゴリズム，数理モデリング
研究業績・著者・論文、その他それに準じる業績	●著書 K. Murota (1987): Systems Analysis by Graphs and Matroids, Springer. K. Murota (2000): Matrices and Matroids for Systems Analysis. Springer. K. Murota (2003): Discrete Convex Analysis, SIAM. 室田一雄 (2001): 離散凸解析. 共立出版. 室田一雄 (2007): 離散凸解析の考えかた，共立出版. 室田一雄，塩浦昭義 (2013): 離散凸解析と最適化アルゴリズム，朝倉書店. 室田一雄，杉原正顯 (2015): 線形代数I，東京大学工学教程（基礎系数学），丸善出版. 室田一雄，杉原正顯 (2013): 線形代数II，東京大学工学教程（基礎系数学），丸善出版. K. Murota and M. Sugihara (2022): Linear Algebra I: Basic Concepts, UTokyo Engineering Course/Basic Mathematics, World Scientific and Maruzen Publishing. K. Murota and M. Sugihara (2022): Linear Algebra II: Advanced Topics for Applications, UTokyo Engineering Course/Basic Mathematics, World Scientific and Maruzen Publishing. 杉原正顯, 室田一雄 (1994): 数値計算法の数理, 岩波書店. 杉原正顯, 室田一雄 (2009): 線形計算の数理, 岩波書店. K. Ikeda and K. Murota (2002): Imperfect Bifurcation in Structures and Materials --- Engineering Use of Group-Theoretic Bifurcation Theory, Springer. K. Ikeda and K. Murota (2010): Imperfect Bifurcation in Structures and Materials --- Engineering Use of Group-Theoretic Bifurcation Theory, Second Edition, Springer. K. Ikeda and K. Murota (2019): Imperfect Bifurcation in Structures and Materials --- Engineering Use of Group-Theoretic Bifurcation Theory,Third Edition, Springer. 池田清宏，室田一雄 (2001): 構造系の座屈と分岐, コロナ社. K. Ikeda and K. Murota (2022): Bifurcation and Buckling in Structures, CRC Press. K. Ikeda and K. Murota (2014): Bifurcation Theory for Hexagonal Agglomeration in Economic Geography, Springer 青本和彦, 上野健爾, 加藤和也, 神保道夫, 砂田利一, 高橋陽一郎, 深谷賢治, 俣野博, 室田一雄編著(2005)：数学入門辞典，岩波書店. など ●論文(離散凸解析に関する論文) K. Murota (1996): Valuated matroid intersection, I: optimality criteria, SIAM Journal on Discrete Mathematics, Vol.9,　pp.545-561. K. Murota (1996): Valuated matroid intersection, II: algorithms, SIAM Journal on Discrete Mathematics, Vol.9, pp.562-576. K. Murota (1996): Convexity and Steinitz's exchange property, Advances in Mathematics, Vol.124, pp.272-311. K. Murota (1998): Fenchel-type duality for matroid valuations, Mathematical Programming, Vol.82, pp. 357--375. K. Murota (1998): Discrete convex analysis, Mathematical Programming, Vol.83, pp.313-371. K. Murota (1999): Submodular flow problem with a nonseparable cost function, Combinatorica, Vol.19, pp.87-109. K. Murota and A. Shioura (1999): M-Convex function on generalized polymatroid, Mathematics of Operations Research, Vol.24, pp.95-105. S. Fujishige and K. Murota (2000): Notes on L-/M-convex functions and the separation theorems, Mathematical Programming, Vol. 88, pp.129-146. K. Murota and A. Shioura (2000): Extension of M-convexity and L-convexity to polyhedral convex functions, Advances in Applied Mathematics, Vol. 25, pp.352-427. V. Danilov, G. Koshevoy, and K. Murota (2001): Discrete convexity and equilibria in economies with indivisible goods and money, Mathematical Social Sciences, Vol.41, pp.251-273. S. Moriguchi, K. Murota and A. Shioura (2002): Scaling algorithms for M-convex function minimization, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E85-A, pp.922-929. S. Moriguchi and K. Murota (2003): Capacity scaling algorithm for scalable M-convex submodular flow problems, Optimization Methods and Software, Vol.18, pp.207--218. K. Murota (2003): On steepest descent algorithms for discrete convex functions, SIAM Journal on Optimization, Vol.14, pp.699-707. K. Murota and A. Tamura (2003): New characterizations of M-convex functions and their applications to economic equilibrium models with indivisibilities, Discrete Applied Mathematics, Vol.131, pp.495-512. K. Murota and A. Tamura (2003):Application of M-convex submodular flow problem to mathematical economics, Japan Journal of Industrial and Applied Mathematics, Vol. 20, pp.257--277. K. Murota and A. Shioura (2003): Quasi M-convex and L-convex functions---Quasi-convexity in discrete optimization, Discrete Applied Mathematics, Vol.~131/132, pp.467-494. H. Hirai and K. Murota (2004): M-convex functions and tree metrics, Japan Journal of Industrial and Applied Mathematics, Vol. 21, pp.391-403. K. Murota and A. Shioura (2004): Conjugacy relationship between M-convex and L-convex functions in continuous variables, Mathematical Programming, Vol.A101, pp.415-433. K. Murota and A. Shioura (2004): Quadratic M-convex and L-convex functions, Advances in Applied Mathematics, Vol.33, pp.318-341. K. Murota and A. Tamura (2004):Proximity theorems of discrete convex functions, Mathematical Programming, Vol.A99, pp.539-562. T. Iimura, K. Murota, and A. Tamura (2005): Discrete fixed point theorem recon-sidered, Journal of Mathematical Economics, Vol.41, pp.1030-1036. S. Iwata, S. Moriguchi and K. Murota (2005): A capacity scaling algorithm for M-convex submodular flow, Mathematical Programming, Vol.103, pp.181-202. S. Moriguchi and K. Murota (2005): Discrete Hessian matrix for L-convex functions, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E88-A, pp.1104-1108. K. Murota (2005): Note on multimodularity and L-convexity, Mathematics of Operations Research, Vol. 30, pp.658-661. K. Murota and A. Shioura (2005): Substitutes and complements in network flows viewed as discrete convexity, Discrete Optimization, Vol. 2, pp.256-268. K. Murota (2006): M-convex functions on jump systems: A general framework for minsquare graph factor problem, SIAM Journal on Discrete Mathematics, Vol. 20, pp.213-226. Y. Kobayashi, K. Murota and K. Tanaka (2007): Operations on M-convex functions on jump systems, SIAM Journal on Discrete Mathematics, Vol. 21, pp.107-129. Y. Kobayashi and K. Murota (2007): Induction of M-convex functions by linking systems, Discrete Applied Mathematics, Vol.155, pp.1471-1480. K. Murota and A. Shioura (2008): Note on the continuity of M-convex and L-convex functions in continuous variables, Journal of the Operations Research Society of Japan, Vol.51, pp.265-273. K. Murota (2009): Recent developments in discrete convex analysis, in: W. Cook, L. Lovasz and J. Vygen, eds., Research Trends in Combinatorial Optimization, Bonn 2008 , Springer, Chapter 11, pp.219-260. K. Murota (2010): Submodular function minimization and maximization in discrete convex analysis, RIMS Kokyuroku Bessatsu, Vol.B23, pp.193-211. Y. Kobayashi, K. Murota and R. Weismantel (2012): Cone superadditivity of discrete convex functions, Mathematical Programming, Series A, Vol. 135, pp.25-44. S. Moriguchi and K. Murota (2012): On discrete Hessian matrix and convex extensibility, Journal of the Operations Research Society of Japan, Vol. 55, pp.48-62. K. Murota and A. Shioura (2014): Dijkstra's algorithm and L-concave function maximization, Mathematical Programming, Series A, Vol.145, pp.163-177. K. Murota and A. Shioura (2014): Exact bounds for steepest descent algorithms of L-convex function minimization, Operations Research Letters, Vol.42, pp.361-366. T. Maehara and K. Murota (2015): A framework of discrete DC programming by discrete convex analysis, Mathematical Programming, Series A, Vol.152, pp.435-466. T. Maehara and K. Murota (2015): Valuated matroid-based algorithm for submodular welfare problem, Annals of Operations Research, Vol.229, pp.565-590. S. Fujishige, K. Murota and A. Shioura (2015): Monotonicity in steepest ascent algorithms for polyhedral L-concave functions, Journal of the Operations Research Society of Japan, Vol.58, pp.184-208. K. Murota (2015): On polyhedral approximation of L-convex and M-convex functions, Journal of the Operations Research Society of Japan, Vol. 58, pp.291-305. K. Murota, and Y. Yokoi (2015): On the lattice structure of stable allocations in two-sided discrete-concave market, Mathematics of Operations Research, Vol. 40, pp.460-473. K. Murota, A. Shioura and Z. Yang (2016): Time bounds for iterative auctions: A unified approach by discrete convex analysis, Discrete Optimization, Vol.19, pp.36-62. K. Murota (2016): Discrete convex analysis: A tool for economics and game theory, Journal of Mechanism and Institution Design, Vol.1, No.1, pp.151-273. K. Murota and A. Shioura (2017): Note on time bounds of two-phase algorithms for L-convex function minimization, Japan Journal of Industrial and Applied Mathematics, Vol. 34, pp.429-440. K. Murota (2018): A stronger multiple exchange property for M#-concave functions, Japan Journal of Industrial and Applied Mathematics, Vol.35, No.1, pp. 411-421. K. Murota and A. Shioura (2018): On equivalence of M#-concavity of a set function and submodularity of its conjugate, Journal of the Operations Research Society of Japan, Vol.61, No.2, pp.163-171. K. Murota and A. Shioura (2018): Simpler exchange axioms for M-concave functions on generalized polymatroids, Japan Journal of Industrial and Applied Mathematics, Vol.35 , No.1, pp.235-259. T. Maehara, N. Marumo, and K. Murota (2018): Continuous relaxation for discrete DC programming, Mathematical Programming, Series B, Vol.169, pp. 199-219 . K. Murota (2018): Multiple exchange property for M#-concave functions and valuated matroids, Mathematics of Operations Research, Vol. 43, No. 3, pp. 781-788. Y. Iwamasa, K. Murota, and S. Zivny (2018): Discrete convexity in joint winner property, Discrete Optimization, Vol.28, pp.78-88. S. Moriguchi, K. Murota, A. Tamura, and F. Tardella (2019): Scaling, proximity, and optimization of integrally convex functions, Mathematical Programming, Vol.175, pp.119-154. M. Bolandnazar, W. T. Huh, S. T. McCormick, and K. Murota (2019): Error noted in ``Order-Based Cost Optimization in Assemble-to-Order Systems'' by Lu and Song (2005), Operations Research, Vol. 67, pp.163-166. S. Moriguchi and K. Murota (2019): Projection and convolution operations for integrally convex functions, Discrete Applied Mathematics, Vol.255, pp.283-298. S. Moriguchi and K. Murota (2019): On fundamental operations for multimodular functions, Journal of the Operations Research Society of Japan, Vol.62, pp.53-63. H. Hirai, Y. Iwamasa, K. Murota, and S.Zivny (2019): A tractable class of binary VCSPs via M-convex intersection, ACM Transactions on Algorithms, Vol.15, No.3, Article 44 (July 2019), 41 pages. Online: https://doi.org/10.1145/3329862 S. Moriguchi, K. Murota, A. Tamura, and F. Tardella (2020): Discrete midpoint convexity, Mathematics of Operations Research,Vol. 45, pp.99-128. K. Murota and A. Tamura (2020): Integrality of subgradients and biconjugates of integrally convex functions, Optimization Letters, Vol.14, pp.195-208. K. Murota and K. Takazawa (2021): Relationship of two formulations for shortest bibranchings, Japan Journal of Industrial and Applied Mathematics, Vol.38, No.1, pp.141-161. K. Murota (2021): A survey of fundamental operations on discrete convex functions of various kinds, Optimization Methods and Software, Vol.36 , Nos.2-3, pp.472-518. K. Murota (2021): On basic operations related to network induction of discrete convex functions, Optimization Methods and Software, Vol.36, Nos.2-3, pp.519-559. K. Murota (2021): A note on M-convex functions on jump systems, Discrete Applied Mathematics, Vol.289, pp.492--502. A. Frank and K. Murota (2022): A discrete convex min-max formula for box-TDI polyhedra, Mathematics of Operations Research, Vol.47, No.2, pp.1026-1047. https://doi.org/10.1287/moor.2021.1160. A. Frank and K. Murota (2022): Decreasing minimization on M-convex sets: Background and Structures, Mathematical Programming, Vol.195, No.1-2, pp.977-1025. https://doi.org/10.1007/s10107-021-01722-2 A. Frank and K. Murota (2022): Decreasing minimization on M-convex sets: Algorithms and applications, Mathematical Programming, Vol.195 , No.1-2, pp.1027-1068. https://doi.org/10.1007/s10107-021-01711-5 K. Murota and A. Tamura (2022): Discrete Fenchel duality for a pair of integrally convex and separable convex functions, Japan Journal of Industrial and Applied Mathematics, Vol.39, No.2, pp.599-630. A. Frank and K. Murota (2022): Fair integral submodular flows, Discrete Applied Mathematics, Vol.320, pp.416-434. A. Frank and K. Murota (2023): Fair integral network flows, Mathematics of Operations Research, Vol.48, No.3, pp. 1393-1422. A. Frank and K. Murota (2023): Decreasing minimization on base-polyhedra: Relation between discrete and continuous cases, Japan Journal of Industrial and Applied Mathematics, Vol.40, No.1, pp.183-221. S. Moriguchi and K. Murota (2023): Note on the polyhedral description of the Minkowski sum of two L-convex sets, Japan Journal of Industrial and Applied Mathematics, Vol.40, No.1, pp.223-263. https://doi.org/10.1007/s13160-022-00512-3 (Open access). S. Moriguchi and K. Murota (2023): Inclusion and intersection relations between fundamental classes of discrete convex functions, Journal of the Operations Research Society of Japan, Vol. 66, No.3, pp.187-217. K. Murota and A. Tamura (2023): Recent progress on integrally convex functions, Japan Journal of Industrial and Applied Mathematics, Vol.40, No.3, pp.1445-1499. https://doi.org/10.1007/s13160-023-00589-4 (Open access) K. Murota and A. Shioura (2024): Note on minimization of quasi M-natural-convex functions, Japan Journal of Industrial and Applied Mathematics, Vol.41 (2024), No.2, *--. https://doi.org/10.1007/s13160-023-00633-3 (Open access) K. Murota and A. Tamura (2024): Decomposition of an integrally convex set into a Minkowski sum of bounded and conic integrally convex sets, Japan Journal of Industrial and Applied Mathematics, Vol.41 (2024), No.2, --*. https://doi.org/10.1007/s13160-023-00635-1 (Open access) など ●論文(初期の論文) K. Murota and K. Takeuchi (1981): The studentized empirical characteristic function and its application to test for the shape of distribution, Biometrika, Vol.68, pp.55-65. Included in: K. Takeuchi: Contributions on Theory of Mathematical Statistics, Springer, 2020, Chapter 9, pp.221-235. K. Murota and M. Iri (1982): Parameter tuning and repeated application of the IMT-type transformation in numerical quadrature, Numerische Mathematik, Vol.38, pp.347-363. K. Murota (1982): Global convergence of a modified Newton iteration for algebraic equations, SIAM Journal on Numerical Analysis, Vol.19, pp.793-799. M. Iri, K. Murota and S. Matsui (1983): Heuristics for planar minimum-weight perfect matchings, Networks, Vol.13, pp.67-92. T. Ohya, M. Iri and K. Murota (1984): Improvements of the incremental method for the Voronoi diagram with computational comparison of various algorithms, Journal of the Operations Research Society of Japan, Vol.27, pp.306-337. K. Murota and M. Iri (1985): Structural solvability of systems of equations---A mathematical formulation for distinguishing accurate and inaccurate numbers in structural analysis of systems, Japan Journal of Applied Mathematics, Vol.2, pp.247-271. K. Murota (1985): Use of the concept of physical dimensions in the structural approach to systems analysis, Japan Journal of Applied Mathematics, Vol.2, pp.471-494. ●詳細は　 http://www.comp.tmu.ac.jp/kzmurota/publist.html
受賞	第２回　日本IBM科学賞（1988年）日本オペレーションズ・リサーチ学会文献賞（1994年）第２１回　井上学術賞（2004年）日本オペレーションズ・リサーチ学会業績賞（2014年）日本応用数理学会業績賞 (2019年) 日本オペレーションズ・リサーチ学会近藤賞（2021年）など
主な学会活動	日本応用数理学会，フェロー日本オペレーションズ・リサーチ学会フェロー，副会長 (2014-2015)
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個人のURL	http://kzmurota.fpark.tmu.ac.jp/
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研究室サイト等	http://kzmurota.fpark.tmu.ac.jp/
取組状況	令和05年度
researchmap	過去の研究業績等(researchmap)