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Discrete Allocation Problems with hard constraints: Study with the aid of discrete convex analysis

Research Project

Project/Area Number 16K00023
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Theory of informatics
Research InstitutionKeio University

Principal Investigator

Tamura Akihisa  慶應義塾大学, 理工学部(矢上), 教授 (50217189)

Co-Investigator(Kenkyū-buntansha) 野寺 隆  慶應義塾大学, 理工学部(矢上), 名誉教授 (50156212)
Project Period (FY) 2016-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords離散資源配分問題 / 離散最適化 / 離散凸解析 / 離散配分問題 / 離散凸関数 / 離散構造 / 情報基礎 / アルゴリズム
Outline of Final Research Achievements

The aims of this research are to deeply study discrete allocation problems with hard constraints by using discrete convex analysis, and to apply theoretical results to problems in the real world. We established five research themes and obtain theoretical results for each theme. On feedback to problems in the real world, we developed software of our two proposed algorithms which have been used to solve the allocation problem of students to departments in our affiliation.

Academic Significance and Societal Importance of the Research Achievements

離散資源配分問題は,学生の学科への配属等の現実問題と強い関係があります.現実的な離散資源配分問題は複雑な制約を有することが多く,これらに対する研究は学術的にも社会的にも意義のあるものです.本研究成果では,良い構造を有する離散凸解析を武器として,理論的な研究成果を得た一方で,複雑な制約を有する学科分け問題という現実問題の解決に理論的成果を応用した点であり,他の現実的な問題への拡大利用も可能であることから,その社会的意義は高いと思われます.

Report

(7 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (30 results)

All 2022 2021 2020 2019 2018 2017 2016 Other

All Int'l Joint Research (7 results) Journal Article (7 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 7 results,  Open Access: 2 results) Presentation (13 results) (of which Int'l Joint Research: 4 results,  Invited: 5 results) Remarks (2 results) Funded Workshop (1 results)

  • [Int'l Joint Research] Simon Fraser University(米国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Stanford University(米国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Etovos Lorand University(ハンガリー)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] University of Oxford(英国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Sapienza University of Rome(イタリア)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Sapienza University of Rome(Italy)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] Sapienza University of Rome(Italy)

    • Related Report
      2016 Research-status Report
  • [Journal Article] Discrete Fenchel duality for a pair of integrally convex and separable convex functions2022

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

      Japan Journal of Industrial and Applied Mathematics

      Volume: - Issue: 2 Pages: 599-630

    • DOI

      10.1007/s13160-022-00499-x

    • NAID

      210000165146

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Directed discrete midpoint convexity2021

    • Author(s)
      Tamura, A. and Tsurumi, K.
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 38 Issue: 1 Pages: 1-37

    • DOI

      10.1007/s13160-020-00416-0

    • NAID

      210000164997

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Integrality of Subgradients and Biconjugates of Integrally Convex Functions2020

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

      Optimization Letters

      Volume: 14 Issue: 1 Pages: 195-208

    • DOI

      10.1007/s11590-019-01501-1

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Discrete midpoint convexity2019

    • Author(s)
      Moriguchi Satoko, Murota Kazuo, Tamura Akihisa, Tardella, Fabio
    • Journal Title

      Mathematics of Operations Research

      Volume: -

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Designing matching mechanisms under constraints: An approach from discrete convex analysis2018

    • Author(s)
      Kojima Fuhito、Tamura Akihisa、Yokoo Makoto
    • Journal Title

      Journal of Economic Theory

      Volume: 176 Pages: 803-833

    • DOI

      10.1016/j.jet.2018.05.004

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Scaling, proximity, and optimization of integrally convex functions2018

    • Author(s)
      Moriguchi, S., Murota, M., Tamura, A. and Tardella, F.
    • Journal Title

      Mathematical Programming

      Volume: -

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] THE STUDENTS/DEPARTMENTS ALLOCATION PROBLEM WITH GROUP CONSTRAINTS — AN APPLICATION OF DISCRETE CONVEX ANALYSIS2017

    • Author(s)
      赤堀峻, 関口陽介, 田村 明久
    • Journal Title

      Transactions of the Operations Research Society of Japan

      Volume: 60 Issue: 0 Pages: 50-73

    • DOI

      10.15807/torsj.60.50

    • NAID

      130006262704

    • ISSN
      1349-8940, 2188-8280
    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Presentation] 離散フェンシェル双対性について2022

    • Author(s)
      田村明久
    • Organizer
      日本オペレーションズリサーチ学会九州支部講演会
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] 整凸関数と分離凸関数に関するフェンシェル双対定理2022

    • Author(s)
      田村明久
    • Organizer
      研究会「モビリティとメカニズムデザイン」
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Fair and Truthful Mechanism with Limited Subsidy2022

    • Author(s)
      H. Goko, A. Igarashi, Y. Kawase, K. Makino, H. Sumita, A. Tamura, Y. Yokoi and M. Yokoo
    • Organizer
      International Conference on Autonomous Agents and Multiagent Systems
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 整凸関数と分離凸関数に対するFenchel双対性2021

    • Author(s)
      室田一雄, 田村明久
    • Organizer
      日本オペレーションズリサーチ学会秋季研究発表会
    • Related Report
      2021 Annual Research Report
  • [Presentation] 有向離散中点凸関数ーL#凸関数の一般化ー2020

    • Author(s)
      鶴身一也*, 田村明久
    • Organizer
      日本オペレーションズリサーチ学会春季研究発表会
    • Related Report
      2019 Research-status Report
  • [Presentation] Discrete Midpoint Convexity and Its Variation2019

    • Author(s)
      田村明久
    • Organizer
      離散凸解析と最適化
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Efficient allocation mechanism with endowments and distributional constraints2018

    • Author(s)
      T. Suzuki, A. Tamura, N. Hamada, M. Yokoo
    • Organizer
      the 17th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2018)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Trading Networks with Bilateral Contracts2018

    • Author(s)
      T. Fleiner, Z. Janko, A. Tamura and A. Teytelboym
    • Organizer
      WINE 2018: The 14th Conference on Web and Internet Economics
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] 離散凸解析を用いたマッチングモデルの展開2018

    • Author(s)
      田村明久
    • Organizer
      離散構造とアルゴリズム
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] 離散凸解析と数理経済モデル2018

    • Author(s)
      田村明久
    • Organizer
      日本数学会2018年度年会
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Algorithms for Discrete Midpoint Convex Functions2018

    • Author(s)
      森口聡子, 室田一雄, 田村明久, Fabio Tardella
    • Organizer
      最適化:モデリングとアルゴリズム
    • Related Report
      2017 Research-status Report
  • [Presentation] Directed Midpoint Convexity2017

    • Author(s)
      S. Moriguchi, K. Murota, A. Tamura, F. Tardella
    • Organizer
      日本オペレーションズリサーチ学会秋季研究発表会
    • Related Report
      2017 Research-status Report
  • [Presentation] Scaling and Proximity Properties of Integrally Convex Functions2016

    • Author(s)
      S. Moriguchi, K. Murota, A. Tamura, F. Tardella
    • Organizer
      The 27th International Symposium on Algorithms and Computation
    • Place of Presentation
      Sydney, Australia
    • Year and Date
      2016-12-12
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Remarks] 慶應義塾大学研究者情報総覧(田村明久のページ)

    • URL

      http://k-ris.keio.ac.jp/Profiles/113/0011208/profile.html

    • Related Report
      2018 Research-status Report
  • [Remarks] 慶應義塾大学研究者情報総覧(田村明久のページ)

    • URL

      http://k-ris.keio.ac.jp/Profiles/113/0011208/profile.html

    • Related Report
      2017 Research-status Report
  • [Funded Workshop] Workshop “Recent Development in Optimization III”2019

    • Related Report
      2019 Research-status Report

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Published: 2016-04-21   Modified: 2023-01-30  

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