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Robust optimization for quasiconvex programming with uncertainty

Research Project

Project/Area Number 15K17588
Research Category

Grant-in-Aid for Young Scientists (B)

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

Principal Investigator

Suzuki Satoshi  島根大学, 総合理工学研究科, 助教 (70580489)

Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords数理計画問題 / 準凸計画問題 / 応用数学 / 凸解析
Outline of Final Research Achievements

Quasiconvex programming problem is one of mathematical programming problems, and has attracted a great deal of attention in recent years as a method for problems which can not be expressed by linear or convex programming problem. On the other hand, when modeling a practical problem into a mathematical model, model uncertainty arising from measurement error etc. occurs, and its response is an important task.
The purpose of this research is to propose robust optimization for quasiconvex programming problem with uncertainty as a method to get a robust and stable solution. Throughout the research period, we studied duality theorems for multiobjective optimization problem with uncertainty, duality theorems and its necessary and sufficient constraint qualifications, optimality conditions and characterizations of the solution set, and properties of quasiconvex functions.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (16 results)

All 2018 2017 2016 2015

All Journal Article (9 results) (of which Peer Reviewed: 9 results,  Open Access: 9 results,  Acknowledgement Compliant: 4 results) Presentation (7 results) (of which Int'l Joint Research: 3 results)

  • [Journal Article] Duality Theorems for Quasiconvex Programming with a Reverse Quasiconvex Constraint2017

    • Author(s)
      Suzuki Satoshi
    • Journal Title

      Taiwanese Journal of Mathematics

      Volume: 21 Issue: 2 Pages: 489-503

    • DOI

      10.11650/tjm/7256

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Quasiconvexity of sum of quasiconvex function2017

    • Author(s)
      Suzuki Satoshi
    • Journal Title

      Linear Nonlinear Analysis

      Volume: 3 Pages: 287-295

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Characterizations of the solution set for non-essentially quasiconvex programming2017

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

      Optimization Letters

      Volume: 11 Issue: 8 Pages: 1699-1712

    • DOI

      10.1007/s11590-016-1084-7

    • NAID

      120006375003

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Generators and constraint qualifications for quasiconvex inequality systems2017

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

      Journal of Nonlinear and Convex Analysis

      Volume: 18 Pages: 2101-2121

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Nonlinear Error Bounds for Quasiconvex Inequality Systems2017

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

      Optimization Letters

      Volume: 11 Issue: 1 Pages: 107-120

    • DOI

      10.1007/s11590-015-0992-2

    • NAID

      120005953893

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Duality theorems for separable convex programming without qualifications2017

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

      Journal of Optimization Theory and Applications

      Volume: 172 Issue: 2 Pages: 669-683

    • DOI

      10.1007/s10957-016-1003-1

    • NAID

      120005973011

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] 準凸解析と最適化理論2016

    • Author(s)
      黒岩 大史, 鈴木 聡
    • Journal Title

      数学

      Volume: 68 Pages: 246-265

    • NAID

      130007420315

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A constraint qualification characterizing surrogate duality for quasiconvex programming2016

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

      Pacific Journal of Optimization

      Volume: 12

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Characterizations of the solution set for quasiconvex programming in terms of Greenberg-Pierskalla subdifferential2015

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

      J. Glob. Optim.

      Volume: 印刷中 Issue: 3 Pages: 431-441

    • DOI

      10.1007/s10898-014-0255-2

    • NAID

      120005647344

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] 逆準凸制約を持つ準凸計画問題について2018

    • Author(s)
      鈴木 聡
    • Organizer
      日本数学会2018年度年会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Quasiconvex programming with a reverse quasiconvex constraint2017

    • Author(s)
      Satoshi Suzuki
    • Organizer
      The 10th Anniversary Conference on Nonlinear Analysis and Convex Analysis
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Nonlinear error bounds in terms of generators of quasiconvex functions2016

    • Author(s)
      Satoshi Suzuki and Daishi 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
      2016-08-31
    • Related Report
      2016 Research-status Report
  • [Presentation] Surrogate duality for quasiconvex vector optimization with data uncertainty2016

    • Author(s)
      Satoshi Suzuki and Daishi Kuroiwa
    • Organizer
      The fifth International Conference on Continuous Optimization
    • Place of Presentation
      National Graduate Institute for Policy Studies, Tokyo, Japan
    • Year and Date
      2016-08-16
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Nonlinear global error bounds for quasiconvex inequality systems2016

    • Author(s)
      Satoshi Suzuki and Daishi Kuroiwa
    • Organizer
      The fifth Asian conference on Nonlinear Analysis and Optimization
    • Place of Presentation
      Toki Messe, Niigata, Japan
    • Year and Date
      2016-08-02
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] 準凸計画問題における解集合の特徴付けについて2015

    • Author(s)
      Suzuki, Satoshi; Kuroiwa, Daishi
    • Organizer
      日本数学会2015年度秋季総合分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-13
    • Related Report
      2015 Research-status Report
  • [Presentation] Necessary and sufficient optimality conditions for quasiconvex programming2015

    • Author(s)
      Suzuki, Satoshi; Kuroiwa, Daishi
    • 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
      2015-09-07
    • Related Report
      2015 Research-status Report

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Published: 2015-04-16   Modified: 2019-03-29  

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