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Methods for Variational Inequalities and Related Problems

Research Project

Project/Area Number 26330029
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical informatics
Research InstitutionNanzan University

Principal Investigator

Fukushima Masao  南山大学, 理工学部, 教授 (30089114)

Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords均衡問題 / 最適化問題 / 変分不等式 / 相補性問題 / ゲーム理論 / 最適化
Outline of Final Research Achievements

Variational inequalities play an important role in mathematical modeling of equilibrium problems that arise in such diverse areas as economics, transportation, finance and mechanics. The purpose of this research is to develop practical methods for problems closely related to variational inequalities, including complementarity problems, optimization problems, and problems in game theory. Specifically, in this research, we developed methods for eigenvalue complementarity problems, multi-leader-follower games, and conic optimization problems such as nonlinear semidefinite programs and nonlinear second-order cone programs.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report

Research Products

(24 results)

All 2018 2017 2016 2015 2014 Other

All Int'l Joint Research (6 results) Journal Article (10 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 10 results,  Open Access: 7 results,  Acknowledgement Compliant: 8 results) Presentation (8 results) (of which Int'l Joint Research: 5 results,  Invited: 4 results)

  • [Int'l Joint Research] University of Coimbra(ポルトガル)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] IMPA(ブラジル)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Instituto Politecnico de Tomar/Instituto de Telecommunicacoes(ポルトガル)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] Virginia Tech(米国)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] University of Coimbra(ポルトガル)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] Instituto de Mathematica Pura e Aplicada(ブラジル)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Optimality conditions for nonlinear semidefinite programming via squared slack variables2018

    • Author(s)
      Bruno Figueira Lourenco, Ellen Hidemi Fukuda and Masao Fukushima
    • Journal Title

      Mathematical Programming

      Volume: 出版予定 Pages: 177-200

    • DOI

      10.1007/s10107-016-1040-4

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Optimality conditions for problems over symmetric cones and a simple augmented Lagrangian method2018

    • Author(s)
      B.F. Lourenco, E.H. Fukuda, M. Fukushima
    • Journal Title

      Mathematics of Operations Research

      Volume: 印刷中

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A note on the squared slack variables technique for nonlinear optimization2017

    • Author(s)
      E.H. Fukuda, M. Fukushima
    • Journal Title

      Journal of the Operations Research Society of Japan

      Volume: 60 Pages: 262-270

    • NAID

      130005874255

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] The second-order cone eigenvalue complementarity problem2016

    • Author(s)
      L.M. Fernandes, M. Fukushima, J.J. Judice and H.D. Sherali
    • Journal Title

      Optimization Methods and Software

      Volume: 31 Pages: 24-52

    • DOI

      10.1080/10556788.2015.1040156

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] The use of squared slack variables in nonlinear second-order cone programming2016

    • Author(s)
      Ellen Hidemi Fukuda and Masao Fukushima
    • Journal Title

      Journal of Optimization Theory and Applications

      Volume: 出版予定 Pages: 394-418

    • DOI

      10.1007/s10957-016-0904-3

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On the quadratic eigenvalue complementarity problem over a general convex cone2015

    • Author(s)
      C.P. Bras, M. Fukushima, A.N. Iusem and J.J. Judice
    • Journal Title

      Applied Mathematics and Computation

      Volume: 271 Pages: 594-608

    • DOI

      10.1016/j.amc.2015.09.014

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Multi-leader-follower games: Models, methods and applications2015

    • Author(s)
      M. Hu and M. Fukushima
    • Journal Title

      Journal of the Operations Research Society of Japan

      Volume: 58 Pages: 1-23

    • NAID

      130005067215

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] On the computation of all eigenvalues for the eigenvalue complementarity problem2014

    • Author(s)
      L.M. Fernandes, J.J. Judice, H.D. Sherali, and M. Fukushima
    • Journal Title

      Journal of Global Optimization

      Volume: 56 Pages: 307-326

    • DOI

      10.1007/s10898-014-0165-3

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] A regularized outer approximation method for monotone semi-infinite variational inequality problems2014

    • Author(s)
      M. Kono and M. Fukushima
    • Journal Title

      Pacific Journal of Optimization

      Volume: 10 Pages: 735-748

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] On the symmetric quadratic eigenvalue complementarity problem2014

    • Author(s)
      L.M. Fernandes, J.J. Judice, M. Fukushimaand A.N. Iusem
    • Journal Title

      Optimization Methods & Software

      Volume: 29 Pages: 751-770

    • DOI

      10.1080/10556788.2013.854359

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] マルチリーダー・フォロワーゲームに対するGauss-Seidel法2018

    • Author(s)
      堀篤史,福島雅夫
    • Organizer
      日本オペレーションズ・リサーチ学会2018年春季研究発表会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Maintenance scheduling of flood control plant under uncertainty based on multi-objective optimization2018

    • Author(s)
      I. Takami, M. Fukushima, F. Yamada, S. Inagaki
    • Organizer
      The 7th International Conference on Industrial Technology and Management (ICITM 2018)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Second-Order Conditions for Nonlinear Semidefinite Optimization Problems via Slack Variables Approach2016

    • Author(s)
      E.H. Fukuda, B.F. Lourenco and M. Fukushima
    • Organizer
      The Fifth International Conference on Continuous Optimization
    • Place of Presentation
      Tokyo, Japan
    • Year and Date
      2016-08-06
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] A Gauss-Seidel Method for Multi-Leader-Follower Games2016

    • Author(s)
      A. Hori and M. Fukushima
    • Organizer
      The Fifth International Conference on Continuous Optimization
    • Place of Presentation
      Tokyo, Japan
    • Year and Date
      2016-08-06
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] マルチ・リーダー・フォロワーゲーム -- 連続最適化の観点から --2016

    • Author(s)
      福嶋雅夫
    • Organizer
      日本オペレーションズ・リサーチ学会春季研究発表会
    • Place of Presentation
      横浜市
    • Year and Date
      2016-03-18
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Go around Complementarity2015

    • Author(s)
      M. Fukushima
    • Organizer
      The 22nd International Symposium on Mathematical Programming
    • Place of Presentation
      Pittsburgh, USA
    • Year and Date
      2015-07-15
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Squared Slack Variables in Nonlinear Second-Order Cone Programming2015

    • Author(s)
      M. Fukushima
    • Organizer
      International Conference on Variational Analysis, Optimization and Quantitative Finance
    • Place of Presentation
      Limoges, France
    • Year and Date
      2015-05-19
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Some results in multi-leader-follower games2014

    • Author(s)
      M. Fukushima
    • Organizer
      Optimization 2014
    • Place of Presentation
      Guimaraes, Portugal
    • Year and Date
      2014-07-29
    • Related Report
      2014 Research-status Report
    • Invited

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Published: 2014-04-04   Modified: 2022-02-16  

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