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2006 Fiscal Year Final Research Report Summary

Research on Numerical Methods for Large-Scale Nonlinear Optimization Problems and their Applications to Software Codes

Research Project

Project/Area Number 16510123
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Social systems engineering/Safety system
Research InstitutionTokyo University of Science

Principal Investigator

YABE Hiroshi  Tokyo University of Science, Faculty of Science, Professor, 理学部, 教授 (90158056)

Co-Investigator(Kenkyū-buntansha) YAMAKI Naokazu  Shizuoka University, Faculty of Engineering, Professor, 工学部, 教授 (20120222)
NUMATA Kazumichi  Tokyo University of Science, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30106893)
OGASAWARA Hideho  Tokyo University of Science, Faculty of Science, Junior Associate Professor, 理学部, 講師 (00231217)
Project Period (FY) 2004 – 2006
Keywordsnonlinear optimization / nonlinear programming / semidefinite programming / conjugate gradient method / memory gradient method / quasi-Newton method / Newton method / primal-dual interior point method
Research Abstract

We have studied numerical methods for solving unconstrained and constrained optimization problems. Specifically, we have done the following.
(1) We have proposed new nonlinear conjugate gradient methods based on the modified secant and the multi-step secant conditions for solving large-scale unconstrained optimization problems. We have proved their global convergence properties. Our numerical experiments show that our proposed methods perform well.
(2) We have proposed a new memory gradient method for solving large-scale unconstrained optimization problems. We have proved their global convergence properties. Our numerical experiments show that our proposed method performs well.
(3) We have combined the limited memory quasi-Newton method, which was proposed by us, and the primal-dual interior point method to solve nonlinearly constrained optimization problems.
(4) We have analyzed local behavior of the primal-dual interior point method for degenerate nonlinear optimization problems.
(5) We have proposed primal-dual interior point methods for solving nonlinear second-order cone programming and nonlinear semidefinite programming problems. We have proved their global convergence properties by using primal-dual merit function within the framework of the line search strategy.
(6) We have proved the local and q-superlinear convergence of the quasi-Newton method with the Broyden family based on the modified secant condition for solving unconstrained optimization problems.
(7) We have dealt with the Barzilai-Borwein method to improve numerical performance of the steepest descent method, and we have proposed the extended Barzilai-Borwein method.

  • Research Products

    (12 results)

All 2007 2006 2005 2004

All Journal Article (12 results)

  • [Journal Article] A primal-dual interior point method for nonlinear semidefinite programming2007

    • Author(s)
      Hiroshi Yamashita
    • Journal Title

      The Institute of Statistical Mathematics, Cooperative Research Report 203

      Pages: 296-317

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Local and superlinear convergence of quasi-Newton methods based on modified secant conditions2007

    • Author(s)
      Hiroshi Yabe
    • Journal Title

      Journal of Computational and Applied Mathematics 205

      Pages: 617-632

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A primal-dual interior point method for nonlinear semidefinite programming2007

    • Author(s)
      H.Yamashita, H.Yabe
    • Journal Title

      The Institute of Statistical Mathematics, Cooperative Research Report 203

      Pages: 296-317

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Local and superlinear convergence of quasi-Newton methods based on modified secant conditions2007

    • Author(s)
      H.Yabe, H.Ogasawara, M.Yoshino
    • Journal Title

      Journal of Computational and Applied Mathematics 205

      Pages: 617-632

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Global convergence of a memory gradient method for unconstrained optimization2006

    • Author(s)
      Yasushi Narushima
    • Journal Title

      Computational Optimization and Applications 35

      Pages: 325-346

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Global convergence of a memory gradient method for unconstrained optimization2006

    • Author(s)
      Y.Narushima, H.Yabe
    • Journal Title

      Computational Optimization and Applications 35

      Pages: 325-346

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Quadratic convergence of a primal-dual interior point method for degenerate nonlinear optimization problems2005

    • Author(s)
      Hiroshi Yamashita
    • Journal Title

      Computational Optimization and Applications 31

      Pages: 123-143

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A new nonlinear conjugate gradient method for unconstrained optimization2005

    • Author(s)
      Hiroshi Yabe
    • Journal Title

      Journal of the Operations Research Society of Japan 48

      Pages: 284-296

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Quadratic convergence of a primal-dual interior point method for degenerate nonlinear optimization problems2005

    • Author(s)
      H.Yamashita, H.Yabe
    • Journal Title

      Computational Optimization and Applications 31

      Pages: 123-143

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A new nonlinear conjugate gradient method for unconstrained optimization2005

    • Author(s)
      H.Yabe, N.Sakaiwa
    • Journal Title

      Journal of the Operations Research Society of Japan 48

      Pages: 284-296

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Global convergence properties of nonlinear conjugate gradient methods with modified secant condition2004

    • Author(s)
      Hiroshi Yabe
    • Journal Title

      Computational Optimization and Applications 28

      Pages: 203-225

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Global convergence properties of nonlinear conjugate gradient methods with modified secant condition2004

    • Author(s)
      H.Yabe, M.Takano
    • Journal Title

      Computational Optimization and Applications 28

      Pages: 203-225

    • Description
      「研究成果報告書概要(欧文)」より

URL: 

Published: 2008-05-27  

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