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Deepening and Expansion of Discrete Convexity Paradigm

Research Project

Project/Area Number 18360048
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionThe 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 *help
¥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.

Report

(5 results)
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (49 results)

All 2009 2008 2007 2006 Other

All Journal Article (25 results) (of which Peer Reviewed: 16 results) Presentation (18 results) Book (4 results) Remarks (2 results)

  • [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

    • Related Report
      2008 Annual Research Report
  • [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

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Note on the continuity of M-convex and L-convex functions in continuous variables2008

    • Author(s)
      K. Murota, A. Shioura
    • Journal Title

      Journal of Operations Research Society of Japan Vol.51, No.4

      Pages: 265-273

    • NAID

      110007008320

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Note on the continuity of M-convex and L-convex functions in continuous variables2008

    • Author(s)
      K.Murota, A.Shioura
    • Journal Title

      Journal of Operations Research Society of Japan 51-4

      Pages: 265-273

    • NAID

      110007008320

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On labor allocation model with possibly bounded salaries2008

    • 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

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The independent even factor problem2008

    • Author(s)
      S.Iwata, K.Takazawa
    • Journal Title

      SIAM Journal on Discrete Mathematics 22-4

      Pages: 1411-1427

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Solving linear programs from sign patterns2008

    • Author(s)
      S.Iwata, N.Kakimura
    • Journal Title

      Mathematical Programming 114

      Pages: 393-418

    • Related Report
      2008 Annual Research Report
    • 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

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Submodular Function Minimization2008

    • Author(s)
      S. Iwata
    • Journal Title

      Mathematical Programming 112

      Pages: 45-64

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Induction of M-convex functions by linking systems2007

    • Author(s)
      Y. Kobayashi, K. Murota
    • Journal Title

      Discrete Applied Mathematics Vol.155

      Pages: 1471-1480

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Combinatorial analysis on singular matrix pencils2007

    • Author(s)
      S. Iwata
    • Journal Title

      SIAM Journal on Matrix Analysis and Applications Vol. 29

      Pages: 245-259

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A two-sided discrete-concave market with possibly bounded side payments : An approach by discrete convex analysis2007

    • Author(s)
      S. Fujishige, A. Tamura
    • Journal Title

      Mathematics of Operations Research Vol.32

      Pages: 136-155

    • Related Report
      2008 Final Research Report
    • 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

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tamura, A two-sided discrete-concave market with possibly bounded side payments: An approach by discrete convex analysis2007

    • Author(s)
      S. Fujishige, A. Tamura
    • Journal Title

      Mathematics of Operations Research 32

      Pages: 136-155

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Combinatorial analysis on singular matrix pencils2007

    • Author(s)
      S. Iwata
    • Journal Title

      SIAM Journal on Matrix Analysis and Applications 29

      Pages: 245-259

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Induction of M-convex Functions by Linking Systems2007

    • Author(s)
      Y. Kobayashi, K. Murota
    • Journal Title

      Discrete Applied Mathematics 155

      Pages: 1471-1480

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Induction of M-convex Functions by Linking Systems2007

    • Author(s)
      Y. Kobayashi and K. Murota
    • Journal Title

      Discrete Applied Mathematics 155

      Pages: 1471-1480

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Linking Systems and Matroid Pencils2007

    • Author(s)
      S. Iwata
    • Journal Title

      Journal of the Operations Research Society of Japan 50

      Pages: 315-324

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Operations on M-convex functions on jump systems2007

    • Author(s)
      Y.Kobayashi, K.Murota, K.Tanaka
    • Journal Title

      SIAM Journal on Discrete Mathematics 21

      Pages: 107-129

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A two-sided discrete-concave market with possibly bounded side payments : An approach by discrete convex analysis2007

    • Author(s)
      S.Fujishige, A.Tamura
    • Journal Title

      Mathematics of Operations Research 32

      Pages: 136-155

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Combinatorial analysis on singular matrix pencils2007

    • Author(s)
      S.Iwata
    • Journal Title

      SIAM Journal on Matrix Analysis and Applications 29

      Pages: 245-259

    • Related Report
      2006 Annual Research Report
  • [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

    • Related Report
      2006 Annual Research Report
  • [Journal Article] steepest descent algorithm for M-convex functions on jump systems, IEICE Transactions on Fundamentals of Electronics2006

    • Author(s)
      K. Murota, K. Tanaka, A
    • Journal Title

      Communications and Computer Sciences Vol. E89-A, No. 5

      Pages: 1160-1165

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] M-convex functions on jump systems : A general framework for minsquare graph factor problem2006

    • Author(s)
      K.Murota
    • Journal Title

      SIAM Journal on Discrete Mathematics 20

      Pages: 213-226

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A steepest descent algorithm for M-convex functions on jump systems2006

    • 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

    • Related Report
      2006 Annual Research Report
  • [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
    • Related Report
      2008 Annual Research Report
  • [Presentation] Discrete convex analysis approach for inventory models2009

    • 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
    • Related Report
      2008 Annual Research Report
  • [Presentation] A simple combinatorial algorithm for submodular function minimization2009

    • 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
    • Related Report
      2008 Annual Research Report
  • [Presentation] Discrete convex analysis---basics and topics2008

    • Author(s)
      K. Murota
    • Organizer
      Oberwolfach Workshop on Combinatorial Optimization
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach
    • Year and Date
      2008-11-11
    • Related Report
      2008 Final Research Report
  • [Presentation] Discrete convex analysis-basics and topics2008

    • Author(s)
      K.Murota
    • Organizer
      Oberwolfach Workshop on Combinatorial Optimization
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach, Germany
    • Year and Date
      2008-11-11
    • Related Report
      2008 Annual Research Report
  • [Presentation] Recent developments in discrete convex analysis2008

    • Author(s)
      K. Murota
    • Organizer
      Bonn Workshop on Combinatorial Optimization
    • Place of Presentation
      University of Bonn
    • Year and Date
      2008-11-06
    • Related Report
      2008 Final Research Report
  • [Presentation] Recent developments in discrete convex analysis2008

    • Author(s)
      K.Murota
    • Organizer
      Bonn Workshop on Combinatorial Optimization
    • Place of Presentation
      University of Bonn, Germany
    • Year and Date
      2008-11-06
    • Related Report
      2008 Annual Research Report
  • [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
    • Related Report
      2007 Annual Research Report
  • [Presentation] Discrete convex functions minimization based on continuous relaxation2008

    • 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
    • Related Report
      2008 Final Research Report
  • [Presentation] Discrete Convex Functions Minimization Based on Continuous Relaxation2008

    • 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
    • Related Report
      2008 Self-evaluation Report 2007 Annual Research Report
  • [Presentation] Minimization of a discrete quasi L-convex function based on continuous relaxation2008

    • Author(s)
      S. Moriguchi, N. Tsuchimura
    • Organizer
      The 4th Sino-Japanese Optimization Meeting
    • Place of Presentation
      National Cheng-Kung University
    • Related Report
      2008 Final Research Report
  • [Presentation] Some topics from discrete convex analysis2008

    • 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
    • Related Report
      2008 Annual Research Report
  • [Presentation] Minimization of a discrete quasi L-convex function based on continuous relaxation2008

    • Author(s)
      S.Moriguchi, N.Tsuchimura
    • Organizer
      The 4th Sino-Japanese Optimization Meeting
    • Place of Presentation
      National Cheng-Kung University, Taiwan
    • Related Report
      2008 Annual Research Report
  • [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
    • Related Report
      2007 Annual Research Report
  • [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
    • Related Report
      2007 Annual Research Report
  • [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
    • Related Report
      2007 Annual Research Report
  • [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
    • Related Report
      2007 Annual Research Report
  • [Presentation] Computational Geometric Approach to Submodular Function Minimization for Multiclass Queueing Systems2007

    • 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
    • Related Report
      2007 Annual Research Report
  • [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.)
    • Related Report
      2008 Final Research Report
  • [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
    • Related Report
      2008 Final Research Report
  • [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
    • Related Report
      2008 Self-evaluation Report
  • [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
    • Related Report
      2007 Annual Research Report
  • [Remarks] 開発したソフトウェアODICON

    • URL

      http://www.misojiro.t.u-tokyo.ac.jp/~tutimura/odicon/

    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      http://www.misojiro.t.u-tokyo.ac.jp/~tutimura/odicon/

    • Related Report
      2008 Annual Research Report

URL: 

Published: 2006-04-01   Modified: 2016-04-21  

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