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Study on duality theory in set-valued programming

Research Project

Project/Area Number 16K05274
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionShimane University

Principal Investigator

Kuroiwa Daishi  島根大学, 学術研究院理工学系, 教授 (40284020)

Project Period (FY) 2016-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords集合値最適化 / 線形スカラー化 / 凸関数 / 拡張凸関数 / 双対理論 / 制約想定 / 集合値計画法 / 埋め込み空間 / 集合値写像 / 埋め込み / 拡張凸性 / 解の特徴付け
Outline of Final Research Achievements

Set-valued optimization problem is a problem to find a set from a family of sets. In this study, we researched theory and methods to find a solution. In particular, we obtained duality results and linear scalarization for this problem. These result nots are not only generalizations of the ordinary mathematical optimization problems and multi-objective optimization problems, but also as a new approach to related fields of various optimization theories such as game theory and mathematical economics.

Academic Significance and Societal Importance of the Research Achievements

本研究成果の学術的な特色は、双対問題を具体的に記述できることである。このことで、これまでに容易に表現出来なかった問題が扱いやすくなる。集合値最適化問題が関連する学問範囲は広く、集合値解析、非線形解析、ベクトル値解析、凸解析、最適化理論、ゲーム理論、ファイナンス等の関連分野への影響力を持つため、国内外を問わず多くの研究者から注目されている研究分野である。従って本研究の発展は関連分野に対しても大きな影響を与え、相乗的に研究が進化・発展すると予想される。

Report

(4 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (32 results)

All 2019 2018 2017 2016 Other

All Int'l Joint Research (13 results) Journal Article (6 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 6 results,  Open Access: 4 results,  Acknowledgement Compliant: 2 results) Presentation (13 results) (of which Int'l Joint Research: 12 results,  Invited: 3 results)

  • [Int'l Joint Research] Martin-Luther Universitat(ドイツ)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Insubria University(イタリア)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Universitatea Babes-Bolyai(ルーマニア)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Naresua University(タイ)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Can Tho University(ベトナム)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Martin-Luther Universitat(Germany)

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

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] Universitatea Babes-Bolyai(Romania)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research]

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] Martin-Luther Universitat(Germany)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] Insubria University(Italy)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] Universitatea Babes-Bolyai(Romania)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research]

    • Related Report
      2016 Research-status Report
  • [Journal Article] Robust optimization: Sensitivity to uncertainty in scalar and vector cases, with applications2018

    • Author(s)
      Crespi Giovanni P.、Kuroiwa Daishi、Rocca Matteo
    • Journal Title

      Operations Research Perspectives

      Volume: 5 Pages: 113-119

    • DOI

      10.1016/j.orp.2018.03.001

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A systematization of convexity and quasiconvexity concepts for set-valued maps, defined by l-type and u-type preoder relations2018

    • Author(s)
      Kazuki Seto, Daishi Kuroiwa and Nicolae Popovici
    • Journal Title

      Optimization

      Volume: 印刷中 Issue: 7 Pages: 1077-1094

    • DOI

      10.1080/02331934.2018.1454920

    • Related Report
      2018 Annual Research Report 2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A fixed set theorem for set-to-set maps2018

    • Author(s)
      Kazuki Seto and Daishi Kuroiwa
    • Journal Title

      Appl. Anal. Optim.

      Volume: 2 Pages: 41-46

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A fixed set theorem for set-to-set maps2018

    • Author(s)
      Kazuki Seto and Daishi Kuroiwa
    • Journal Title

      Applied Analysis and Optimization

      Volume: 2 Pages: 41-46

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Generalized set order relations and their numerical treatment2017

    • Author(s)
      E. Kobis, D. Kuroiwa, and C. Tammer
    • Journal Title

      Applied Analysis and Optimization

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Lagrange-type duality in DC programming problems with equivalent DC inequalities2016

    • Author(s)
      R. Harada and D. Kuroiwa
    • Journal Title

      Journal of Inequalities and Applications

      Volume: 2016:276 Issue: 1 Pages: 1-15

    • DOI

      10.1186/s13660-016-1219-5

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] A linear scalarization and duality results for convex set optimization2019

    • Author(s)
      Daishi Kuroiwa
    • Organizer
      SOFA2019
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Duality for convex set optimization2018

    • Author(s)
      Daishi Kuroiwa
    • Organizer
      NAO-ASIA 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A duality result for convex set optimization2018

    • Author(s)
      Daishi Kuroiwa
    • Organizer
      ACFPTO 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A duality theorem for convex set optimization2018

    • Author(s)
      Daishi Kuroiwa
    • Organizer
      ICVANO 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Set optimization and its duality idea2017

    • Author(s)
      Daishi Kuroiwa
    • Organizer
      NACA
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Nash equilibria of repeated multi-objective games2017

    • Author(s)
      Makoto Kanehara and Daishi Kuroiwa
    • Organizer
      NACA
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] A characterization of cone-quasiconvexity for set-valued maps2017

    • Author(s)
      Kazuki Seto and Daishi Kuroiwa
    • Organizer
      NACA
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] An observation of constraint qualifications for duality of DC optimization problems2017

    • Author(s)
      Takumi Murakami, Yuya Sumida, Daishi Kuroiwa
    • Organizer
      非線形解析学と凸解析学の研究
    • Related Report
      2017 Research-status Report
  • [Presentation] Robust Vector Optimization: Well-Posedness, Sensitivity to Uncertainty and Generalized Convexity of Set-valued Maps2016

    • Author(s)
      C. Giovanni, D. Kuroiwa, N. Popovici, and M. Rocca
    • Organizer
      ICCOPT 2016
    • Place of Presentation
      National Graduate Institute for Policy Studies, Tokyo Japan
    • Year and Date
      2016-08-06
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Unified Approach in Set Optimization and Generalized Convexity for Set-valued Maps2016

    • Author(s)
      D. Kuroiwa
    • Organizer
      ICCOPT 2016
    • Place of Presentation
      National Graduate Institute for Policy Studies, Tokyo Japan
    • Year and Date
      2016-08-06
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Generalized Convexity for Set-valued Maps and Its Applications2016

    • Author(s)
      K. Seto and D. Kuroiwa
    • Organizer
      ICCOPT 2016
    • Place of Presentation
      National Graduate Institute for Policy Studies, Tokyo Japan
    • Year and Date
      2016-08-06
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Surrogate Duality for Quasiconvex Vector Optimization with Data Uncertainty2016

    • Author(s)
      S. Suzuki and D. Kuroiwa
    • Organizer
      ICCOPT 2016
    • Place of Presentation
      National Graduate Institute for Policy Studies, Tokyo Japan
    • Year and Date
      2016-08-06
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Unied approach in set optimization with parameterized embedding functions2016

    • Author(s)
      D. Kuroiwa
    • Organizer
      NAO Asia 2016
    • Place of Presentation
      Toki Messe, Niigata, Japan
    • Year and Date
      2016-08-01
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited

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Published: 2016-04-21   Modified: 2020-03-30  

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