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Development of practical derivative-free algorithms for optimization

Research Project

Project/Area Number 25330022
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical informatics
Research InstitutionUniversity of Tsukuba

Principal Investigator

Kuno Takahito  筑波大学, システム情報系, 教授 (00205113)

Co-Investigator(Kenkyū-buntansha) AKIKO YOSHISE  筑波大学, システム情報系, 教授 (50234472)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords数理計画法 / 非線形最適化 / 大域的最適化 / 最適化アルゴリズム / 分枝限定法 / 数理最適化 / 確定的アルゴリズム
Outline of Final Research Achievements

The major results of this research are two deterministic algorithms for solving concave minimization problems to global optimality. The one belongs to the class of branch-and-bound algorithms, referred to as the conical algorithm, which subdivides the feasible set using a number of cones and computes a lower bound of the objective function on each. We developed a new rule for cone subdivision, named w-bisection, and proved the convergence of the algorithm according to it. Our numerical experiments indicated that our new subdivision rule is rather promising. The other is a kind of simplicial algorithm which subdivides the feasible set using simplices and carries out lower-bounding on each. We generalized existing w-subdivision, w-bisection, and proposed w-k-section. Under this simplex subdivision rule, we proved the convergence of the algorithm, and implemented numerical experiments, which demonstrated an advantage of w-k-section compared with other existing subdivision rules.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (8 results)

All 2016 2015 2014 2013

All Journal Article (5 results) (of which Peer Reviewed: 2 results,  Acknowledgement Compliant: 2 results) Presentation (3 results) (of which Invited: 1 results)

  • [Journal Article] A generalization of ω-subdivision ensuring convergence of the simplicial algorithm2016

    • Author(s)
      T. Kuno, and T. Ishihama
    • Journal Title

      Computational Optimization and Applications

      Volume: online Issue: 2 Pages: 1-21

    • DOI

      10.1007/s10589-015-9817-6

    • NAID

      120007135411

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On the complexity of the stable marriage problem for restricted instance classes2016

    • Author(s)
      Y. Igarashi, T. Kuno, and Y. Sano
    • Journal Title

      数理解析研究所講究録

      Volume: 1981 Pages: 117-126

    • Related Report
      2015 Annual Research Report
  • [Journal Article] A convergent conical algorithm with ω-bisection for concave minimization2015

    • Author(s)
      T.Kuno, and T.Ishihama
    • Journal Title

      Journal of Global Optimization

      Volume: 61 Issue: 2 Pages: 203-220

    • DOI

      10.1007/s10898-014-0197-8

    • NAID

      120007130389

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A convergent conical algorithm with w-bisection for concave minimization2013

    • Author(s)
      T.Kuno, and T.Ishihama
    • Journal Title

      CS Technical Report

      Volume: CS-TR-13-20 Pages: 1-20

    • Related Report
      2013 Research-status Report
  • [Journal Article] A simplicial algorithm with w-ksections and its convergence2013

    • Author(s)
      T.Kuno, and T.Ishihama
    • Journal Title

      数理解析研究所講究録

      Volume: 1879 Pages: 97-116

    • Related Report
      2013 Research-status Report
  • [Presentation] 入力に制限を与えた安定結婚問題の計算複雑性について2016

    • Author(s)
      五十嵐悠,久野誉人,佐野良夫
    • Organizer
      日本OR学会2016年春季研究発表会
    • Place of Presentation
      慶應義塾大学矢上キャンパス (神奈川県)
    • Year and Date
      2016-03-17
    • Related Report
      2015 Annual Research Report
  • [Presentation] A convergent subdivision rule for the simplicial algorithm2014

    • Author(s)
      T.Kuno
    • Organizer
      Workshop on Equilibrium and Fixed Point Problems Theory and Algorithms
    • Place of Presentation
      Vietnam Institute for Advanced Study in Mathematics (ベトナム)
    • Year and Date
      2014-08-25 – 2014-08-26
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] w-k分割による単体分枝限定法とその収束性2013

    • Author(s)
      久野誉人,石濱友裕
    • Organizer
      京都大学数理解析研究所研究集会「最適化の基礎理論と応用」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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