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Study of the entire solution set and preference solutions in set-valued programming

Research Project

Project/Area Number 19K03637
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12040:Applied mathematics and statistics-related
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) 2019-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2021: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2020: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2019: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords集合値最適化 / 重み付け法 / 大域的評価法 / 集合値計画法 / スカラー化 / 選好解 / 集合値計画問題 / 解集合の特徴付け / 双対理論 / 凸性 / 線形スカラー化 / 解集合
Outline of Research at the Start

多様な価値観を自然に表現することが可能な集合値計画問題の最適解に関して、解全体の書き上げに関する研究、すなわち解集合の特徴付けについての研究、および意思決定者が「望ましい」と感じる解、すなわち選好解についての研究を行うことである。これらは、インタラクティブ(対話的)に解を求める際に必要な理論であり、多目的計画問題においては研究がなされているものの、集合値計画問題においては数学的な土壌の欠如のため、未だ十分な研究がなされていない。従って、まずは限定的な埋め込み空間とその双対空間についての基礎的な研究から行い、本研究のために必要となる数学的な土壌を醸成する。

Outline of Final Research Achievements

Set-valued programming problem is a problem to find a set from a family of sets. In this study, we research about preferred solutions for the decision maker. We obtained results about kinds of the weighting method and the global criterion method for set optimization. By using these methods, "hidden" solutions can be found from the previous scalarization methods. These results are not only generalizations of 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

多目的最適化の拡張であり、実社会において頻繁に現れる問題の解を、意思決定者の好みで解を用意に見つけることが出来る。

Report

(6 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (19 results)

All 2021 2020 2019 Other

All Int'l Joint Research (10 results) Journal Article (5 results) (of which Int'l Joint Research: 5 results,  Peer Reviewed: 5 results,  Open Access: 5 results) Presentation (4 results) (of which Int'l Joint Research: 3 results,  Invited: 1 results)

  • [Int'l Joint Research] チェンマイ大学/ナレスワン大学/モンクット王工科大学トンブリー校(タイ)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] インスブリア大学/カルロ・カッターネオ大学/ボッコーニ大学(イタリア)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] Univ Insubria(イタリア)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Naresuan Univ(タイ)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Cantho Univ/Ton Duc Thang Univ/Vietnam Natl Univ Ho Chi Minh City(ベトナム)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Univ Lancaster(英国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Insubria University(イタリア)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Naresuan University/Bansomdejchaopraya Rajabhat University(タイ)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Nam Can Tho University/Vietnam National University/Ton Duc Thang University(ベトナム)

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

    • Related Report
      2019 Research-status Report
  • [Journal Article] On the properties of lexicographic tolerable robust solution sets for uncertain multi-objective optimization problems2021

    • Author(s)
      BORIWAN PORNPIMON, KUROIWA DAISHI, PETROT NARIN
    • Journal Title

      Carpathian Journal of Mathematics

      Volume: 38 Issue: 1 Pages: 57-66

    • DOI

      10.37193/cjm.2022.01.06

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Convergence of Solutions to Set Optimization Problems with the Set Less Order Relation2020

    • Author(s)
      Anh Lam Quoc、Duy Tran Quoc、Hien Dinh Vinh、Kuroiwa Daishi、Petrot Narin
    • Journal Title

      Journal of Optimization Theory and Applications

      Volume: 185 Issue: 2 Pages: 416-432

    • DOI

      10.1007/s10957-020-01657-2

    • Related Report
      2020 Research-status Report 2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Robust Nash equilibria in vector-valued games with uncertainty2020

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

      Annals of Operations Research

      Volume: 289 Issue: 2 Pages: 185-193

    • DOI

      10.1007/s10479-020-03563-2

    • Related Report
      2020 Research-status Report 2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] The Lexicographic Tolerable Robustness Concept for Uncertain Multi-Objective Optimization Problems: A Study on Water Resources Management2020

    • Author(s)
      Boriwan Pornpimon、Ehrgott Matthias、Kuroiwa Daishi、Petrot Narin
    • Journal Title

      Sustainability

      Volume: 12 Issue: 18 Pages: 7582-7582

    • DOI

      10.3390/su12187582

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Surrogate duality for optimization problems involving set functions2019

    • Author(s)
      Kuroiwa, Daishi; Lee, Gue Myung; Suzuki, Satoshi
    • Journal Title

      Linear Nonlinear Anal.

      Volume: 5 Pages: 269-277

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] 集合最適化問題の選好解について2021

    • Author(s)
      黒岩大史
    • Organizer
      RIMS 共同研究(公開型) 非線形解析学と凸解析学の研究
    • Related Report
      2021 Research-status Report
  • [Presentation] A linear scalarization and prefered solutions for set optimization2019

    • Author(s)
      Daishi Kuroiwa
    • Organizer
      naca-icota2019
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Set optimization and its prefered solutions2019

    • Author(s)
      Daishi Kuroiwa
    • Organizer
      Nonlinear Analysis and Convex Analysis, RIMS Workshop
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Duality for set optimization and prefered solutions2019

    • Author(s)
      Daishi Kuroiwa
    • Organizer
      IWANA 2019
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited

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Published: 2019-04-18   Modified: 2025-01-30  

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