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A notions of directional derivative for set-valued maps on set optimization programming and its applications

Research Project

Project/Area Number 19540130
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionShimane University

Principal Investigator

KUROIWA Daishi  Shimane University, 総合理工学部, 准教授 (40284020)

Co-Investigator(Kenkyū-buntansha) 田中 環  新潟大学, 自然科学系, 教授 (10207110)
松下 慎也  松江工業高等専門学校, 電子工学科, 助教 (20435449)
山内 貴光  島根大学, 総合理工学部, 教務職員 (00403444)
Co-Investigator(Renkei-kenkyūsha) TANAKA Tamaki  新潟大学, 自然科学系, 教授 (10207110)
YAMAUCHI Takamitsu  島根大学, 総合理工学部, 講師 (00403444)
MATSUSHITA Shin-ya  秋田県立大学, システム科学技術学部, 助教 (20435449)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords集合値最適化 / 微分概念 / 多目的最適化 / 数理計画法 / 集合値計画法 / 数理計画 / 微分 / 集合値解析学
Research Abstract

We study optimization problems whose objective maps are set-valued maps based on criteria called 'set optimization.' We introduce a quotient space of a family of sets with an equivalence relation, we show the set optimization problems are embedded in the space, and we consider methodology to find solutions.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (41 results)

All 2010 2009 2008 2007 Other

All Journal Article (24 results) (of which Peer Reviewed: 15 results) Presentation (17 results)

  • [Journal Article] On derivatives and convexity of set-valued maps and optimality conditions in set optimization2009

    • Author(s)
      D. Kuroiwa
    • Journal Title

      Journal of Nonlinear and Convex Analysis 1

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Set containment characterization for quasiconvex programming2009

    • Author(s)
      S. Suzuki, D. Kuroiwa
    • Journal Title

      Journal of Global Optimization 45

      Pages: 551-563

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Set optimization theory and its applications2009

    • Author(s)
      D. Kuroiwa
    • Journal Title

      International workshop on computational intelligence & applications proceedings

      Pages: 267-269

    • NAID

      120006658682

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Set containment characterization and mathematical programming2009

    • Author(s)
      S. Suzuki, D. Kuroiwa
    • Journal Title

      International workshop on computational intelligence & applications proceedings

      Pages: 264-266

    • NAID

      120006658681

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 関数の生成集合について2009

    • Author(s)
      Y. Seno, M. Tsubokura, D. Kuroiwa
    • Journal Title

      関数の生成集合について 1643

      Pages: 207-211

    • Related Report
      2009 Final Research Report
  • [Journal Article] 集合の包含に関する一般化された結果とその適用例2009

    • Author(s)
      S. Suzuki, D. Kuroiwa
    • Journal Title

      RIMS Kokyuroku 1643

      Pages: 134-138

    • Related Report
      2009 Final Research Report
  • [Journal Article] On derivatives of set-valued maps and optimality conditions for set optimization2009

    • Author(s)
      Daishi Kuroiwa
    • Journal Title

      J.Nonlinear Convex Anal. 10

      Pages: 41-50

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Set optimization theory and its applications2009

    • Author(s)
      Daishi Kuroiwa
    • Journal Title

      International workshop on computational intelligence & applications proceedings

      Pages: 267-269

    • NAID

      120006658682

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Set containment characterization for quasiconvex programming2009

    • Author(s)
      Satoshi Suzuki, Daishi Kuroiwa
    • Journal Title

      J.Global Optim. 45

      Pages: 551-563

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 関数の生成集合について2009

    • Author(s)
      Yoshiyuki Seno, Masae Tsubokura, Daishi Kuroiwa
    • Journal Title

      RIMS Kokyuroku 1643

      Pages: 207-211

    • Related Report
      2009 Annual Research Report
  • [Journal Article] An evaluation of efficient points for vector optimization2008

    • Author(s)
      T. Nuriya, D. Kuroiwa
    • Journal Title

      Taiwanese Journal of Math. 12

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On derivatives of set-valued maps in set optimization2008

    • Author(s)
      D. Kuroiwa
    • Journal Title

      RIMS Kokyuroku 1611

      Pages: 51-55

    • Related Report
      2009 Final Research Report
  • [Journal Article] Characterizing set containments with quasiconvex inequalities2008

    • Author(s)
      S. Suzuki, D. Kuroiwa
    • Journal Title

      RIMS Kokyuroku 1611

      Pages: 56-60

    • Related Report
      2009 Final Research Report
  • [Journal Article] An evaluation of efficient points for vector optimization2008

    • Author(s)
      Tetsuya Nuriya, Daishi Kuroiwa
    • Journal Title

      Taiwanese J. Math. 8

      Pages: 2063-2082

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] ON DERIVATIVES OF SET-VALUED MAPS IN SET OPTIMIZATTON2008

    • Author(s)
      Daishi Kuroiwa
    • Journal Title

      RIMS Kokyuroku 1161

      Pages: 51-55

    • Related Report
      2008 Annual Research Report
  • [Journal Article] CHARACTERIZING SET CONTAINMENTS WITH QUASICONVEX INEQUALITIES2008

    • Author(s)
      Satoshi Suzuki, Daishi Kuroi wa
    • Journal Title

      RIMS Kokyuroku 1161

      Pages: 56-60

    • Related Report
      2008 Annual Research Report
  • [Journal Article] A generalized embedding vector space in set optimization2007

    • Author(s)
      D. Kuroiwa, T. Nuriya
    • Journal Title

      Proceedings of the Forth International Conference on Nonlinear Analysis and Convex Analysis(Yokohama Publ., Yokohama)

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A topology on the embedding space in set optimization2007

    • Author(s)
      T. Nuriya, D. Kuroiwa
    • Journal Title

      Proceedings of the Forth International Conference on Nonlinear Analysis and Convex Analysis, Yokohama Publ., Yokohama

      Pages: 497-503

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Observation on various conjugates of quasiconvex functions2007

    • Author(s)
      S. Suzuki, M. Kurokawa, D. Kuroiwa
    • Journal Title

      IMS Kokyuroku 1544

      Pages: 206-211

    • Related Report
      2009 Final Research Report
  • [Journal Article] On an equivalence relation between efficiency2007

    • Author(s)
      T. Nuriya, D. Kuroiwa
    • Journal Title

      RIMS Kokyuroku 1544

      Pages: 212-215

    • Related Report
      2009 Final Research Report
  • [Journal Article] A generalized embedding vector space in set optimization2007

    • Author(s)
      Daishi Kuroiwa
    • Journal Title

      Nonlinear analysts and conuexanalysis

      Pages: 497-503

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence theorems for set-valued operators in Banach spaces2007

    • Author(s)
      Shin-ya Matsushita
    • Journal Title

      Set-Valued Analysis 15

      Pages: 251-264

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Characterization of metrizable finitistic space and its applications to upper semicontinuouis set-valued selections2007

    • Author(s)
      Takamitsu Yamauchi
    • Journal Title

      Houston J. Math 33

      Pages: 735-751

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized characterizations of set containments for a certain class of quasiconvex functions

    • Author(s)
      S. Suzuki, D. Kuroiwa
    • Journal Title

      Nonlinear Analysis and Optimization

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Presentation] Set optimization theory2010

    • Author(s)
      D. Kuroiwa
    • Organizer
      Seminars on applied mathematics
    • Place of Presentation
      National sun yat-sen university, Taiwan.
    • Year and Date
      2010-03-22
    • Related Report
      2009 Final Research Report
  • [Presentation] Set optimization theory2010

    • Author(s)
      D. Kuroiwa
    • Organizer
      Workshop on optimization analysis and its applications
    • Place of Presentation
      Tsing Hua, Taiwan
    • Year and Date
      2010-03-20
    • Related Report
      2009 Final Research Report
  • [Presentation] Set optimization and duality theorems2009

    • Author(s)
      D. Kuroiwa
    • Organizer
      AHA2009
    • Place of Presentation
      Kaohsiung, Taiwan.
    • Year and Date
      2009-12-19
    • Related Report
      2009 Final Research Report
  • [Presentation] Set optimization and duality theorems2009

    • Author(s)
      Daishi Kuroiwa
    • Organizer
      Abstract Harmonic Analysis 2009
    • Place of Presentation
      Kaohshiung, Taiwan
    • Year and Date
      2009-12-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] Set optimization theory and its applications2009

    • Author(s)
      D. Kuroiwa
    • Organizer
      International workshop on computational intelligence & applications 2009
    • Place of Presentation
      Higashi Hiroshima, Japan.
    • Year and Date
      2009-11-11
    • Related Report
      2009 Final Research Report
  • [Presentation] Set optimization theory and its applications2009

    • Author(s)
      Daishi Kuroiwa
    • Organizer
      International workshop on computational intelligence & applications 2009
    • Place of Presentation
      Higashi Hiroshima, Japan
    • Year and Date
      2009-11-11
    • Related Report
      2009 Annual Research Report
  • [Presentation] Set optimization theory and its applications2009

    • Author(s)
      D. Kuroiwa
    • Organizer
      nternational workshop on Institutional supply chain management
    • Place of Presentation
      Xian, China.
    • Year and Date
      2009-08-09
    • Related Report
      2009 Final Research Report
  • [Presentation] Set optimization theory and its applications2009

    • Author(s)
      Daishi Kuroiwa
    • Organizer
      International workshop on Institutional supply chain management
    • Place of Presentation
      Xi'an, China
    • Year and Date
      2009-08-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] Constraint Qualification for Set Optimization Programming2009

    • Author(s)
      D. Kuroiwa
    • Organizer
      NACA2009
    • Place of Presentation
      Tokyo, Japan.
    • Year and Date
      2009-03-30
    • Related Report
      2009 Final Research Report
  • [Presentation] On Directional Derivatives in Set Optimization2008

    • Author(s)
      D. Kuroiwa
    • Organizer
      NAO-Asia 2008
    • Place of Presentation
      Matsue, Japan.
    • Year and Date
      2008-09-15
    • Related Report
      2009 Final Research Report
  • [Presentation] Optimality Conditions for Set Optimization Problems with Derivatives of Set-Valued Maps2008

    • Author(s)
      D. Kuroiwa
    • Organizer
      WCNA2008
    • Place of Presentation
      Florida, USA.
    • Year and Date
      2008-07-08
    • Related Report
      2009 Final Research Report
  • [Presentation] Optimality Condi tions for Set Opt imizat ion Problems with Derivatives for Set-Valued Maps2008

    • Author(s)
      Daishi Kuroiwa
    • Organizer
      WCNA2008
    • Place of Presentation
      Florida, USA
    • Year and Date
      2008-07-08
    • Related Report
      2008 Annual Research Report
  • [Presentation] On derivatives of set-valued maps in set optimization and its applications2007

    • Author(s)
      D. Kuroiwa
    • Organizer
      ICOTA2007
    • Place of Presentation
      Kobe, Japan.
    • Year and Date
      2007-12-15
    • Related Report
      2009 Final Research Report
  • [Presentation] Onderivatives for set-valued maps and its applications2007

    • Author(s)
      Daishi Kuroiwa
    • Organizer
      ICOTA7
    • Place of Presentation
      Kobe, Japan
    • Year and Date
      2007-12-15
    • Related Report
      2007 Annual Research Report
  • [Presentation] On Derivatives for Set-Valued Maps and Its applications2007

    • Author(s)
      D. Kuroiwa
    • Organizer
      ISNACA2007
    • Place of Presentation
      NSYSU, Kaohsiung, Taiwan.
    • Year and Date
      2007-11-24
    • Related Report
      2009 Final Research Report
  • [Presentation] On Derivatives of Set-Valued Maps in Set Optimization2007

    • Author(s)
      D. Kuroiwa
    • Organizer
      非線形解析学と凸解析学の研究
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-09-03
    • Related Report
      2009 Final Research Report
  • [Presentation] On Derivatives of Set-Valued Maps and Optimality in Set Optimization2007

    • Author(s)
      D. Kuroiwa
    • Organizer
      NACA2007
    • Place of Presentation
      National sun yat-sen university, Taiwan.
    • Year and Date
      2007-05-31
    • Related Report
      2009 Final Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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