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Reconstruction of variational analysis through industrial mathematics

Research Project

Project/Area Number 22740057
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionTokyo University of Marine Science and Technology

Principal Investigator

SEKIGUCHI Yoshiyuki  東京海洋大学, 海洋科学技術研究科, 准教授 (50434890)

Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords変分解析 / 最適化理論 / 関数解析 / 代数幾何 / 最適化問題 / 凸代数幾何 / 関数解析学 / 解析学 / 数理工学 / アルゴリズム
Research Abstract

We considered quantitative analysis of metric regularity in variational analysis and inequality systems on Banach spaces by functional analytic methods. In addition, we studied theoretical properties of a algorithm for obtaining a global minimum of polynomial optimization problems. Our main results are the following:
1. We gave a formula for modulus of regularity of inequality systems on the space of continuous function. 2. We improved estimates of performance of an SRPT scheduling algorithm by optimization methods in function spaces. 3. An algorithm for obtaining a global minimum of polynomial optimization problems generates a sequence of semidefinite programming problems. We gave sufficient conditions for such semidefinite programming problems to have strong duality properties.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (16 results)

All 2013 2012 2011 2010

All Journal Article (7 results) (of which Peer Reviewed: 3 results) Presentation (9 results) (of which Invited: 1 results)

  • [Journal Article] Real ideal and the duality of semidefinite programming for polynomial optimization2013

    • Author(s)
      Y. Sekiguchi, T. Takenawa, H. Waki
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 30 Pages: 321-330

    • NAID

      10031185311

    • Related Report
      2013 Final Research Report
  • [Journal Article] Real ideal and the duality of semidefinite programming for polynomial optimization2013

    • Author(s)
      Yoshiyuki Sekiguchi, Tomoyuki Takenawa and Hayato Waki
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 20 Issue: 2 Pages: 321-330

    • DOI

      10.1007/s13160-013-0104-6

    • NAID

      10031185311

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An improved analysis of SRPT scheduling algorithm on the basis of functional optimization2012

    • Author(s)
      H. Fujiwara, Y. Sekiguchi
    • Journal Title

      Information Processing Letters

      Volume: 112 Pages: 911-915

    • NAID

      120007100507

    • Related Report
      2013 Final Research Report
  • [Journal Article] An improved analysis of SRPT scheduling algorithm on the basis of functional optimization2012

    • Author(s)
      Hiroshi Fujiwara, Yoshiyuki Sekiguchi
    • Journal Title

      Information Processing Letters

      Volume: 112 Issue: 23 Pages: 911-915

    • DOI

      10.1016/j.ipl.2012.08.009

    • NAID

      120007100507

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Average-case competitive analyses for one-way trading2011

    • Author(s)
      H. Fujiwara, K. Iwama, Y. Sekiguchi
    • Journal Title

      Journal of Combinatorial Optimization

      Volume: 21 Pages: 83-107

    • NAID

      120007100508

    • Related Report
      2013 Final Research Report
  • [Journal Article] Average-Case Competitive Analyses for One-Way Trading2011

    • Author(s)
      H.Fujiwara, K.Iwama, Y.Sekiguchi
    • Journal Title

      Journal of Combinatorial Optimization

      Volume: Vol.21 Pages: 83-107

    • NAID

      120007100508

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Exact estimates of the regularity modulus for infinite programming2010

    • Author(s)
      Y. Sekiguchi
    • Journal Title

      Mathematical Programming

      Volume: 123 Pages: 253-263

    • Related Report
      2013 Final Research Report
  • [Presentation] Real ideal and duality, Mathematics, Algorithms and Proofs 20122012

    • Author(s)
      Y. Sekiguchi
    • Organizer
      Young researcher's session
    • Place of Presentation
      Konstanz, Germany
    • Year and Date
      2012-09-18
    • Related Report
      2013 Final Research Report
  • [Presentation] 凸代数幾何と最適化理論2012

    • Author(s)
      関口良行
    • Organizer
      Mathematical Economics Monday Seminar in Keio University
    • Place of Presentation
      東京
    • Year and Date
      2012-04-16
    • Related Report
      2013 Final Research Report
  • [Presentation] 凸代数幾何 と最適化理論2012

    • Author(s)
      関口 良行
    • Organizer
      Mathematical Economics Monday Seminar in Keio University
    • Place of Presentation
      慶應大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Real ideal and duality of polynomial optimization2012

    • Author(s)
      Yoshiyuki Sekiguchi
    • Organizer
      Young Researcher's session at Mathematics, Algorithms and Proofs 2012
    • Place of Presentation
      University of Konstanz, Germany
    • Related Report
      2012 Annual Research Report
  • [Presentation] Real ideal and duality related to polynomial optimization, Optimization : theory2011

    • Author(s)
      Y. Sekiguchi
    • Organizer
      algorithms and applications in economics
    • Place of Presentation
      Barcelona
    • Year and Date
      2011-10-27
    • Related Report
      2013 Final Research Report
  • [Presentation] Real ideal and duality related to polynomial optimization2011

    • Author(s)
      Yoshiyuki Sekiguchi
    • Organizer
      Optimization : theory, algorithms and applications in economics
    • Place of Presentation
      Barcelona, Spain
    • Year and Date
      2011-10-27
    • Related Report
      2011 Annual Research Report
  • [Presentation] 無限次元変分解析の理論とオンライン アルゴリズムにおける応用例2010

    • Author(s)
      関口良行
    • Organizer
      Ramp シンポジウム
    • Place of Presentation
      名古屋
    • Year and Date
      2010-10-29
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] 無限次元変分解析の理論とオンラインアルゴリズムにおける応用例2010

    • Author(s)
      関口良行
    • Organizer
      Rampシンポジウム
    • Place of Presentation
      名古屋大学(愛知県)
    • Year and Date
      2010-10-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] Real ideal and duality related to polynomial optimization2010

    • Author(s)
      Y. Sekiguchi
    • Organizer
      Mathematical Economics Monday Seminar in Keio University
    • Place of Presentation
      東京
    • Year and Date
      2010-04-19
    • Related Report
      2013 Final Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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