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Studies on Development and Synthesis of Efficient Algorithms for Optimization and Equilibrium Problems

Research Project

Project/Area Number 08650079
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionKYOTO UNIVERSITY

Principal Investigator

FUKUSHIMA Masao  Kyoto University, Grad. School of Engineering, Professor, 工学研究科, 教授 (30089114)

Co-Investigator(Kenkyū-buntansha) YAMAKAWA Eiki  Takamatsu University, Faculty of Management, Lecturer, 経営学部, 講師 (20289333)
TAJI Kouichi  Nara Institute of Science and Technology, Grad. School of Information Sci., Assi, 情報科学研究科, 助手 (00252833)
IBARAKI Satoru  Kyoto University, Grad. School of Engineering, Assistant Professor, 工学研究科, 助手 (10252488)
Project Period (FY) 1996 – 1997
Project Status Completed (Fiscal Year 1997)
Budget Amount *help
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1997: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1996: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsOptimization / Equilibrium Model / Algorithm / Variational Inequality Problem / Complementarity Problem
Research Abstract

Variational inequality and complementarity problems are fundamental problems that are very useful in formulating various equilibrium problems arising not only in engineering such as transportation, structural mechanics and operations reseach but also in social sciences such as economics. In this project, we have conducted research on those fundamental equilibrium problems with particular emphasis on the optimization reformulation approach that have recently attracted much attention in this field. The main results which have been obtained during the last two years are summarized as follows :
1.New approaches that reformulate variational inequality and complementarity problems as equivalent optimization problems have been proposed. Moreover novel algorithms that extend descent methods and Newton's method have been developed, and their effectiveness has been examined through extensive numerical experiments.
2.New parallel and decomposition methods for variational inequality and complementarity problems have been developed by meking use of the idea of operator splitting and matrix splitting.
3.New algorithms have been developed for solving mathematical program with equilibrium constraints for which a unified study has not been done so far.

Report

(3 results)
  • 1997 Annual Research Report   Final Research Report Summary
  • 1996 Annual Research Report
  • Research Products

    (33 results)

All Other

All Publications (33 results)

  • [Publications] M.Fukushima: "Merit functions for variational inequality and complementarity problems" Nonlinear Optimization and Applications. 155-170 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Taji: "A new merit function and a successive quadratic programming algorithm for variational inequality problems," SIAM Journal on Optimization. 6. 704-713 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Yamashita: "Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems" Mathematical Programming. 76. 469-491 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Yamashita: "Equivalent unconstrained minimization and global error bounds for variational inequality problems" SIAM Journal on Control and Optimization. 35. 273-284 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] M.Fukushima: "Minimizing and stationary sequences of merit functions for complementarity problems and variational inequalities" Complementarity and Variational Problems : State of the Arts. 91-104 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Yamashita: "Unconstrained optimization reformulations of variational inequality problems" Journal of Optimization Theory and Applications. 92. 439-456 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Taji and M.Fukushima: "A new merit function and a successive quadratic programming algorithm for variational inequality problems" SIAM Journal on Optimization. 6. 704-713 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Yamashita and M.Fukushima: "Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems" Mathematical Programming. (Series B)76. 469-491 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Yamashita and M.Fukushima: "Equivalent unconstrained minimization and global error bounds for variational inequality problems" SIAM Journal on Control and Optimization. 35. 273-284 (1977)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] M.Fukushima and J.-S.Pang: "Minimizing and stationary sequences of merit functions for complementarity problems and variational inequalities" Complementarity and Variational Problems : State of the Arts, M.C.Ferris and J.-S.Pang(eds.), SIAM,Philadelphia. 91-104 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Yamashita, K.Taji and M.Fukushima: "Unconstrained optimization reformulations of veriational inequality problems" Journal of Optimization Theory and Application. 92. 439-456 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] M.Fukushima: Merit functions for variational inequality and complementarity problems, Nonlinear Optimization and Applications, G.Di Pillo and F.Giannessi(eds.). Plenum Press, 155-170 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Yamashita and M.Fukushima: "Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems" Mathematical Programming. 76. 469-491 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Yamashita and M.Fukushima: "Equivalent unconstrained minimization and global error bounds for variationainequality problems" SIAM Journal on Control and Optimization. 35. 273-284 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] M.Fukushima and J.-S.Pang: "Minimizing and stationary sequences of merit functions for complementarity problems and variational inequalities" Complementarity and Variational Problems : State of the Arts. 91-104 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] D.Sun, M.Fukushima and L.Qi.: "A computable generalized Hessian of the D-gap function and Newton-type methods for variational inequality problems" Complementarity and Variational Problems : State of the Arts. 452-472 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Yamashita. K.Taji and M.Fukushima: "Unconstrained optimization reformulations of variational inequality problems" Journal of Optimization Theory and Applications. 92. 439-456 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 山川栄樹, 牧英一, 福島雅夫: "分離可能な2次計画問題に対する非同期型ブロック並列アルゴリズム" システム制御情報学会論文誌. 10. 248-258 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] C.Kanzow, N.Yamashita and M.Fukushima: "New NCP-functions and their properties" Journal of Optimization Theory and Applications. 94. 115-135 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Jiang, M.Fukushima, L.Qi and D.Sun: "A trust region method for solving generalized complementarity problems" SIAM Journal on Optimization. (掲載予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] M.Fukushima and J.-S.Pang: "Some feasibility issues in mathematical programs with equilibrium constraints" SIAM Journal on Optimization. (掲載予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] M.Fukushima: "Parallel variable transformation in unconstrained optimization" SIAM Journal on Optimization. (掲載予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] M.Fukushima, Z.-Q. Luo and J.S.Pang: "A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints" Computational Optimization and Applications. (掲載予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] C.Kanzow and M.Fukushima: "Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities" Mathematical Programming. (掲載予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] C.Kanzow: "Equivalence of the generalized complementarity problem to differentiable unconstrained minimization" J.Opt.Theory and Appl.90・3. 581-603 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Fukushima: "A globally and superlinearly convergont algorithm for nonsmocth eonvex minimization" SIAM J.Opt.6・4. 1106-1120 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] N.Yamashita: "Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems" Math.Programming. (発表予定).

    • Related Report
      1996 Annual Research Report
  • [Publications] N.Yamashita: "Equivalent unconstrained minimization and global error bounds for variational ineguality problems" SIAM J.Control and Opt.(発表予定).

    • Related Report
      1996 Annual Research Report
  • [Publications] N.Yamashita: "Unconstrained optimization reformulations of variational inequality Problems" J.Opt Theory and Appl.(発表予定).

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Fukushima: "Minimizing and stationary sequences of merit functions for complementarity problems and variational inequalities" Complementarity and Variational Problems:State of the Art. (発表予定).

    • Related Report
      1996 Annual Research Report
  • [Publications] D.Sun: "A computable generalized Hessian of the D-gap function and Newton-type methods for variational inequality problems" Complementarity and Variational Problems:State of the Art. (発表予定).

    • Related Report
      1996 Annual Research Report
  • [Publications] C.Kanzow: "New NCP-functions and their properties" J.Opt Theory and Appl.(発表予定).

    • Related Report
      1996 Annual Research Report
  • [Publications] H.Jiang: "A trust region method for solving generalized complementarity problems" SIAM J.Opt.(発表予定).

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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