Deepening and Expansion of Discrete Convexity Paradigm

• Project/Area Number: 18360048
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Engineering fundamentals
• Research Institution: The University of Tokyo
• Principal Investigator: MUROTA Kazuo The University of Tokyo, 大学院・情報理工学系研究科, 教授 (50134466)
• Co-Investigator(Kenkyū-buntansha): TAMURA Akihisa 慶応義塾大学, 理工学部, 教授 (50217189) ; IWATA Satoru 京都大学, 数理解析研究所, 教授 (00263161) ; TSUCHIMURA Nobuyuki 関西学院大学, 理工学部, その他(教育技術職員) (20345119) ; MORIGUCHI Satoko 産業技術大学院大学, 産業技術研究科, 助教 (60407351)
• Co-Investigator(Renkei-kenkyūsha): SHIOURA Akiyoshi 東北大学, 大学院・情報科学研究科, 准教授 (10296882)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥13,260,000 (Direct Cost: ¥11,100,000、Indirect Cost: ¥2,160,000); Fiscal Year 2008: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2007: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2006: ¥3,900,000 (Direct Cost: ¥3,900,000)
• Keywords: 離散最適化 / 凸関数 / 双対性 / 劣モジュラ関数 / マトロイド

Research Abstract

経済学,システム工学,最適化理論,アルゴリズム理論などの広汎な分野における基礎的諸問題に関わる離散構造を,離散凸性という横断的視点から整理し,「離散凸」という新しいパラダイムを確立し,それを広範囲の応用分野に浸透させる研究を行った.「離散凸パラダイム」の横糸を成す,構造定理やアルゴリズムを代表とする離散関数に関する数理の研究と,縦糸を成す,諸応用分野における具体的な諸問題に対する研究を行った.

Research Products

• [Journal Article] (2009)
  • Author(s): 室田一雄
  • Journal Title: 最適化の理論を創る:離散凸解析,「数理工学 最新ツアーガイド…応用から生まれつつある新しい数学」(杉原正顯, 杉原厚吉編)(日本評論社) Pages: 47-78
• [Journal Article] (2009)
  • Author(s): 室田一雄
  • Journal Title: Recent developments in discrete convex analysis, in : W.Cook, L.Lovasz and J.Vygen, eds., Research Trends in Combinatorial Optimization(Springer-Verlag) Pages: 219-260
• [Journal Article] Note on the continuity of M-convex and L-convex functions in continuous variables (2008)
  • Author(s): K. Murota, A. Shioura
  • Journal Title: Journal of Operations Research Society of Japan Vol.51, No.4 Pages: 265-273
  • NAID: 110007008320
  • Peer Reviewed
• [Journal Article] Note on the continuity of M-convex and L-convex functions in continuous variables (2008)
  • Author(s): K.Murota, A.Shioura
  • Journal Title: Journal of Operations Research Society of Japan 51-4 Pages: 265-273
  • NAID: 110007008320
  • Peer Reviewed
• [Journal Article] On labor allocation model with possibly bounded salaries (2008)
  • Author(s): R.Farooq, Y.T.Ikebe, A.Tamura
  • Journal Title: Journal of Operations Research Society of Japan 51-2 Pages: 136-154
  • NAID: 110006792049
  • Peer Reviewed
• [Journal Article] The independent even factor problem (2008)
  • Author(s): S.Iwata, K.Takazawa
  • Journal Title: SIAM Journal on Discrete Mathematics 22-4 Pages: 1411-1427
  • Peer Reviewed
• [Journal Article] Solving linear programs from sign patterns (2008)
  • Author(s): S.Iwata, N.Kakimura
  • Journal Title: Mathematical Programming 114 Pages: 393-418
  • Peer Reviewed
• [Journal Article] (2008)
  • Author(s): 室田一雄
  • Journal Title: Discrete mathematics, in : H.Araki, ed., Mathematics : Concepts and Foundations, Vol.3, Encyclopedia of Life Support Systems(Eolss Publishers Co., Ltd./UNESCO) Pages: 135-178
• [Journal Article] Submodular Function Minimization (2008)
  • Author(s): S. Iwata
  • Journal Title: Mathematical Programming 112 Pages: 45-64
  • Peer Reviewed
• [Journal Article] Induction of M-convex functions by linking systems (2007)
  • Author(s): Y. Kobayashi, K. Murota
  • Journal Title: Discrete Applied Mathematics Vol.155 Pages: 1471-1480
  • Peer Reviewed
• [Journal Article] Combinatorial analysis on singular matrix pencils (2007)
  • Author(s): S. Iwata
  • Journal Title: SIAM Journal on Matrix Analysis and Applications Vol. 29 Pages: 245-259
  • Peer Reviewed
• [Journal Article] A two-sided discrete-concave market with possibly bounded side payments : An approach by discrete convex analysis (2007)
  • Author(s): S. Fujishige, A. Tamura
  • Journal Title: Mathematics of Operations Research Vol.32 Pages: 136-155
  • Peer Reviewed
• [Journal Article] 連続/離散ハイブリッドM凸関数に関する一考察 (2007)
  • Author(s): 森口聡子, 原辰次, 室田一雄
  • Journal Title: システム制御情報学会論文誌 Vol. 20 Pages: 84-86
  • NAID: 10022000132
  • Peer Reviewed
• [Journal Article] Tamura, A two-sided discrete-concave market with possibly bounded side payments: An approach by discrete convex analysis (2007)
  • Author(s): S. Fujishige, A. Tamura
  • Journal Title: Mathematics of Operations Research 32 Pages: 136-155
  • Peer Reviewed
• [Journal Article] Combinatorial analysis on singular matrix pencils (2007)
  • Author(s): S. Iwata
  • Journal Title: SIAM Journal on Matrix Analysis and Applications 29 Pages: 245-259
  • Peer Reviewed
• [Journal Article] Induction of M-convex Functions by Linking Systems (2007)
  • Author(s): Y. Kobayashi, K. Murota
  • Journal Title: Discrete Applied Mathematics 155 Pages: 1471-1480
  • Peer Reviewed
• [Journal Article] Induction of M-convex Functions by Linking Systems (2007)
  • Author(s): Y. Kobayashi and K. Murota
  • Journal Title: Discrete Applied Mathematics 155 Pages: 1471-1480
  • Peer Reviewed
• [Journal Article] Linking Systems and Matroid Pencils (2007)
  • Author(s): S. Iwata
  • Journal Title: Journal of the Operations Research Society of Japan 50 Pages: 315-324
  • Peer Reviewed
• [Journal Article] Operations on M-convex functions on jump systems (2007)
  • Author(s): Y.Kobayashi, K.Murota, K.Tanaka
  • Journal Title: SIAM Journal on Discrete Mathematics 21 Pages: 107-129
• [Journal Article] A two-sided discrete-concave market with possibly bounded side payments : An approach by discrete convex analysis (2007)
  • Author(s): S.Fujishige, A.Tamura
  • Journal Title: Mathematics of Operations Research 32 Pages: 136-155
• [Journal Article] Combinatorial analysis on singular matrix pencils (2007)
  • Author(s): S.Iwata
  • Journal Title: SIAM Journal on Matrix Analysis and Applications 29 Pages: 245-259
• [Journal Article] 連続/離散ハイブリッドM凸関数に関する一考察 (2007)
  • Author(s): 森口聡子, 原辰次, 室田一雄
  • Journal Title: システム制御情報学会論文誌 20 Pages: 84-86
  • NAID: 10022000132
• [Journal Article] steepest descent algorithm for M-convex functions on jump systems, IEICE Transactions on Fundamentals of Electronics (2006)
  • Author(s): K. Murota, K. Tanaka, A
  • Journal Title: Communications and Computer Sciences Vol. E89-A, No. 5 Pages: 1160-1165
  • Peer Reviewed
• [Journal Article] M-convex functions on jump systems : A general framework for minsquare graph factor problem (2006)
  • Author(s): K.Murota
  • Journal Title: SIAM Journal on Discrete Mathematics 20 Pages: 213-226
• [Journal Article] A steepest descent algorithm for M-convex functions on jump systems (2006)
  • Author(s): K.Murota, K.Tanaka
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E89-A Pages: 1160-1165
  • NAID: 110007502826
• [Presentation] 離散凸解析とその応用 (2009)
  • Author(s): 森口聡子
  • Organizer: 日本オペレーションズ・リサーチ学会2009年春季研究発表会
  • Place of Presentation: 筑波大学
  • Year and Date: 2009-03-18
• [Presentation] Discrete convex analysis approach for inventory models (2009)
  • Author(s): 森口聡子
  • Organizer: International Symposium of Case Studies involving Statistics and Operations Research for Decision Making : Solving Human Problems in Business, Society, and Scientific Areas
  • Place of Presentation: 統計数理研究所
  • Year and Date: 2009-03-02
• [Presentation] A simple combinatorial algorithm for submodular function minimization (2009)
  • Author(s): S.Iwata, J.B.Orlin
  • Organizer: The 20th Annual ACM-SIAM Symposium on Discrete Algorithms
  • Place of Presentation: New York, U.S.A.
  • Year and Date: 2009-01-06
• [Presentation] Discrete convex analysis---basics and topics (2008)
  • Author(s): K. Murota
  • Organizer: Oberwolfach Workshop on Combinatorial Optimization
  • Place of Presentation: Mathematisches Forschungsinstitut Oberwolfach
  • Year and Date: 2008-11-11
• [Presentation] Discrete convex analysis-basics and topics (2008)
  • Author(s): K.Murota
  • Organizer: Oberwolfach Workshop on Combinatorial Optimization
  • Place of Presentation: Mathematisches Forschungsinstitut Oberwolfach, Germany
  • Year and Date: 2008-11-11
• [Presentation] Recent developments in discrete convex analysis (2008)
  • Author(s): K. Murota
  • Organizer: Bonn Workshop on Combinatorial Optimization
  • Place of Presentation: University of Bonn
  • Year and Date: 2008-11-06
• [Presentation] Recent developments in discrete convex analysis (2008)
  • Author(s): K.Murota
  • Organizer: Bonn Workshop on Combinatorial Optimization
  • Place of Presentation: University of Bonn, Germany
  • Year and Date: 2008-11-06
• [Presentation] 離散準L凸関数最小化における連続緩和 (2008)
  • Author(s): 土村 展之, 森口 聡子
  • Organizer: 統計数理研究所研究集会「最適化:モデリングとアルゴリズム」
  • Place of Presentation: 統計数理研究所(東京都港区)
  • Year and Date: 2008-03-18
• [Presentation] Discrete convex functions minimization based on continuous relaxation (2008)
  • Author(s): S. Moriguchi, N. Tsuchimura
  • Organizer: Ninth International Conference Approximation and Optimization in the Caribbean-APPOPT' 2008
  • Place of Presentation: San Andres Island
  • Year and Date: 2008-03-04
• [Presentation] Discrete Convex Functions Minimization Based on Continuous Relaxation (2008)
  • Author(s): S. Moriguchi, N. Tsuchimura
  • Organizer: Ninth International Conference Approximation and Optimization in the Caribbean-APPOPT'2008
  • Place of Presentation: San Andres Island
  • Year and Date: 2008-03-04
• [Presentation] Minimization of a discrete quasi L-convex function based on continuous relaxation (2008)
  • Author(s): S. Moriguchi, N. Tsuchimura
  • Organizer: The 4th Sino-Japanese Optimization Meeting
  • Place of Presentation: National Cheng-Kung University
• [Presentation] Some topics from discrete convex analysis (2008)
  • Author(s): K.Murota
  • Organizer: Kyoto RIMS Workshop on Combinatorial Optimization and Discrete Algorithms
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] Minimization of a discrete quasi L-convex function based on continuous relaxation (2008)
  • Author(s): S.Moriguchi, N.Tsuchimura
  • Organizer: The 4th Sino-Japanese Optimization Meeting
  • Place of Presentation: National Cheng-Kung University, Taiwan
• [Presentation] 離散凸関数最小化における連続緩和と近接定理 (2007)
  • Author(s): 森口 聡子
  • Organizer: 日本オペレーションズ・リサーチ学会計算と最適化研究部会(S@CO)発表会
  • Place of Presentation: 上智大学(東京都千代田区)
  • Year and Date: 2007-12-15
• [Presentation] M〓/L〓凸関数最小化における連続緩和の実験的評価 (2007)
  • Author(s): 森口 聡子, 土村 展之
  • Organizer: 日本オペレーションズ・リサーチ学会秋季研
  • Place of Presentation: 政策研究大学院大学(東京都港区)
  • Year and Date: 2007-09-28
• [Presentation] 連続緩和を用いた離散凸関数最小化 (2007)
  • Author(s): 森口 聡子, 土村 展之
  • Organizer: 日本応用数理学会2007年度年会
  • Place of Presentation: 北海道大学工学部(北海道札幌市)
  • Year and Date: 2007-09-17
• [Presentation] 離散凸関数に対する連続緩和を用いた最小化アルゴリズム (2007)
  • Author(s): 土村 展之, 森口 聡子
  • Organizer: 日本オペレーションズリサーチ学会創立50周年記念事業SSOR2007
  • Place of Presentation: 伊東ホテル聚楽(静岡県伊東市)
  • Year and Date: 2007-08-31
• [Presentation] Computational Geometric Approach to Submodular Function Minimization for Multiclass Queueing Systems (2007)
  • Author(s): T.ItokoandS.Iwata
  • Organizer: The Twelfth International Conference on Integer Programming and Combinatorial Optimization(IPCO)
  • Place of Presentation: Cornell University
  • Year and Date: 2007-06-26
• [Book] Research Trends in Combinatorial Optimization, (Recent developments in discrete convex analysis) (2009)
  • Author(s): K. Murota
  • Publisher: Springer-Verlag(W. Cook, L. Lovasz, J. Vygen, eds.)
• [Book] 離散凸解析の考えかた---最適化における離散と連続の数理 (2007)
  • Author(s): 室田一雄
  • Publisher: 共立出版
• [Book] 離散凸解析の考えかた-最適化における離散と連続の数理 (2007)
  • Author(s): 室田一雄
  • Total Pages: 252
  • Publisher: 共立出版
• [Book] 離散凸解析の考えかた-最適化における離散と連続の数理 (2007)
  • Author(s): 室田 一雄
  • Total Pages: 252
  • Publisher: 共立出版
• [Remarks] 開発したソフトウェアODICON
  • URL: http://www.misojiro.t.u-tokyo.ac.jp/~tutimura/odicon/
• [Remarks]
  • URL: http://www.misojiro.t.u-tokyo.ac.jp/~tutimura/odicon/