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Numerical Methods for Nonsmooth Equations

Research Project

Project/Area Number 14540118
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 InstitutionHirosaki University

Principal Investigator

CHEN Xiaojun  Hirosaki University, Faculty of Science and Technology, Professor, 理工学部, 教授 (70304251)

Co-Investigator(Kenkyū-buntansha) KURATSUBO Shigehiko  Hirosaki University, Faculty of Science and Technology, Professor, 理工学部, 教授 (50003512)
FUKUSHIMA Masao  Kyoto University, Graduate School of Informatics, Professor, 情報学研究科, 教授 (30089114)
KUROIWA Daishi  Shimane University, Faculty of Science and Technology, Lecture, 総合理工学部, 講師 (40284020)
Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2003: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2002: ¥1,700,000 (Direct Cost: ¥1,700,000)
Keywordsnonsmooth equation / numerical methods / verification method / complementary problem / saddle problem / optimal control problem / optimization algorithm / numerical methods for diffeiential equations / 非線形方程式 / 滑らかでない / Karlsruhe大学 / Maryland大学 / 最適化
Research Abstract

In 2003, the head investigator published 4 papers. Among these papers, a single authored paper is published in SIAM Journal on Control and Optimization, a top level journal in optimization area. Moreover, the head investigator edited a special issue of Journal of Computational and Applied Mathematics with Prof.G.Alefeld and Prof.T.Yamamoto.
Some research results are briefly summarized as follows.
1.The head investigator developed an efficient algorithm for solving stochastic linear complementarity problems with Prof.Masao Fukushima, and presented a Keynote lecture m the international workshop on Risk Management and Optimization in Beijing, December 2003.
2.The head investigator proposed a verification method for linear/nonlinear saddle point problems with Mr.Hashimoto who was a Master student of the head investigator and now is a Ph.D student in Kyushu University.
3.The head investigator found some important properties on nonsmooth optimal control problems, and presented the results in the annual meeting of Mathematical Society of Japan, September 2003.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (19 results)

All Other

All Publications (19 results)

  • [Publications] X.Chen, H.Hashimoto: "Numerical validation of solutions of saddle point matrix equations"Numerical Linear Algebra with Applications. 10. 661-672 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] X.Chen, H.Hashimoto: "Verification methods for nonlinear equations with saddle point functions"Journal of Computational and Applied Mathematics. 159. 13-24 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] X.Chen: "First order conditions for nonsmooth discretized constrained optimal control"SIAM J.Control and Optimization. 42. 2004-2015 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] X.Chen, M.Fukushima: "A smoothing method for a mathematical program with P-matrix linear complementarity constraints"Computational optimization and Applications. 27. 223-246 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] X.Chen: "First order conditions for nonsmooth discretized optimal control"SIAM J.Control Optimization. 42. 2004-2015 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] X.Chen, H.Hashimoto: "Numerical validation of solutions of saddle point Matrix equations"Numerical Linear Algebra with Applications. 10. 661-672 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] X.Chen, M.Fukushima: "A smoothing method for a mathematical program With P-matrix linear complementarity constraints"Computational Optimization. 27. 223-246 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] X.Chen, H.Hashimoto: "Verification methods for nonlinear equations with Saddle point functions"Journal of Computational and. 159. 13-24 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] X.Chen, H.Hashimoto: "Verification methods for nonlinear equations with saddle point functions"Journal of Computational and Applied Mathematics. 159. 13-24 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] X.Chen, H.Hashimoto: "Numerical validation of solutions of saddle anoint matrix equations"Numerical Linear Algebra with Applications. 10. 661-672 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] X.Chen, M.Fukushima: "A smoothing method for a mathematical program with P-matrix linear complementarity constraints"Computational Optimization and Applications. 27. 223-246 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] X.Chen: "First order conditions for nonsmooth discretized constrained optimal control"SIAM J.Control and Optimization. 42. 2004-2015 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] X.Chen: "Applications of smoothing methods in numerical analysis and optimization,"Journal of Asian Information Science Life. 1. 1-13 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] G.E.Alefeld, X.Chen, F.A.Potra: "Numerical validation of solutions of complementarity problems : The nonlinear case"Numerische Mathematik. 92. 1-16 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] X.Chen: "On convergence of SOR methods for nonsmooth equations"Numerical Linear Algebra with Applications. 9. 81-92 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] X.Chen, L.Qi, Y.Yang: "Lagrangian globalization methods for nonlinear complementarity problems,"Journal of Optimization Theory and Applications. 112. 77-95 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] B.Mermri, X.Chen: "On characterizations and regularity of the solution of bilateral obstacle problems"Journal of Computational and Applied Mathematics. (印刷中). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Z.wei, L.Qi, X.Chen: "An SQP-type method and its application in stochastic programs,"Journal of Optimization Theory and Applications. 116. 205-228 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] G.Alefeld, X.Chen, T.Yamamoto: "Recent Advances in Computational Mathematics, Journal of Computational and Applied Mathematics"Elsevier Science Publishers, North-Holland. 250 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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