教員紹介参照<参照>

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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 ・離散凸解析の理論と応用に関して,イタリア,イギリス,ハンガリーなどの海外研究者と共同研究を行った.
・離散凸関数の基本性質を精査・整理し,サーベイ論文に纏めた.
・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,英文図書の執筆に取り組んだ.
・群論的分岐理論の英文書籍(2002年第1版,2010年第2版)を大幅に改訂して,第3版としてSpringerより出版した.
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.

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 (2021): A discrete convex min-max formula for box-TDI polyhedra, Mathematics of Operations Research, published on-line https://doi.org/10.1287/moor.2021.1160.

A. Frank and K. Murota (2021): Decreasing minimization on M-convex sets: Background and Structures, Mathematical Programming, Published online https://doi.org/10.1007/s10107-021-01722-2

A. Frank and K. Murota (2021): Decreasing minimization on M-convex sets: Algorithms and applications, Mathematical Programming, Published online https://doi.org/10.1007/s10107-021-01711-5

S. Moriguchi and K. Murota (2021): Note on the polyhedral description of the Minkowski sum of two L-convex sets, arXiv: https://arxiv.org/abs/2110.10445

S. Moriguchi and K. Murota (2021): Inclusion and intersection relations between fundamental classes of discrete convex functions, arXiv: https://arxiv.org/abs/2111.07240

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://www.comp.tmu.ac.jp/kzmurota
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://www.comp.tmu.ac.jp/kzmurota/
取組状況 令和02年度
researchmap 過去の研究業績等(researchmap)