• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Development of polynomial-time algorithms for solving non-monotone complementarity problems

Research Project

Project/Area Number 13650061
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionUniversity of Tsukuba

Principal Investigator

YOSHISE Akiko  University of Tsukuba, Institute of Policy and Planning Sciences, Associate Professor, 社会工学系, 助教授 (50234472)

Co-Investigator(Kenkyū-buntansha) SHIGENO Maiko  University of Tsukuba, Institute of Policy and Planning Sciences, Assistant Professor, 社会工学系, 講師 (40272687)
TAKAHITO Kuno  University of Tsukuba, Institute of Information Sciences and Electronics, Associate Professor, 電子・情報工学系, 助教授 (00205113)
YAMAMOTO Yoshitsugu  University of Tsukuba, Institute of Policy and Planning Sciences, Professor, 社会工学系, 教授 (00119033)
ANDO Kazutoshi  Shizuoka University, Department of Systems Engineering, Associate Professor, 工学部, 助教授 (00312819)
SATO-ILIC Mika  University of Tsukuba, Institute of Policy and Planning Sciences, Associate Professor, 社会工学系, 助教授 (60269214)
Project Period (FY) 2001 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2003: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2002: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2001: ¥1,100,000 (Direct Cost: ¥1,100,000)
KeywordsComplementarity problem / Optimization / Polynomial-time algorithm / Interior point method / Homogeneous method / 多項式時間性
Research Abstract

The complementarity problem is a problem to find a non negative vectors (x, y) which satisfy the equality constraint y=f(x) and the complementarity condition. While some pseudo polynomial-time algorithms have been developed for monotone mappings f, it is known diet the problem with a PO mapping f is NP-complete even if f is linear. However, many problems arising from the real world have been formulated into PO complementarily problems. The aim of the research is to develop some efficient algorithms for solving these practical but non-monotone complementarity problems. To attain it, we provide a homogeneous, interior point method which can be applicable to the complementarity problems with PO functions, derive its theoretical properties and develop a practical algorithm. We consider that we have attained the aim of the research by providing a new algorithm leaving some desirable properties concerning its convergence

Report

(4 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (27 results)

All Other

All Publications (27 results)

  • [Publications] 反町宏明, 吉瀬章子: "サポートベクターマシンにおけるカーネル行列の最適化"統計数理研究所共同研究レポート「最適化-モデリングとアルゴリズム」. 17. 253-275 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] N.Thoai, Y.Yamamoto, A.Yoshise: "Global Optimization Method for Solving Mathematical Programs with Linear Complementarity Constraints"Journal of Optimization Theory and Applications. 124(印刷中). (2005)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 吉瀬章子: "A homogeneous model for PO and P* nonlinear complementarity problems"統計数理研究所共同研究レポート「最適化モデリングとアルゴリズム」. 16. 200-220 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Iwata, M.Shigeno: "Conjugate Scaling Technique for Feanchel-Type Duality in Discrete Convex Optimization"SIAM Journal on Optimization. 13. 204-211 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] J.Gotoh, N.Thoai, Y.Yamamoto: "Global Optimization Method for Solving the Minimum Maximal Flow Problem"Optimization Method and Software. 18. 395-415 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Hotta, A.Yoshise: "A complexity bound of a predictor-corrector smoothing method using CHKS-functions for monotone LCP"Computational Optimization and Applications. 22. 351-367 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 吉瀬章子 著: "応用数理計画ハンドブック(理論編 線形計画法)(久保幹雄, 田村明久, 松井知己 編)"朝倉書店. 1354 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Sorimachi, A.Yoshise: "Optimization of the kernel matrix in the support vector machine"The Institute of Statistics and Mathematics Co-operative Report, Optimization : Modeling and Algorithms. 17. 253-275 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] N.Thoai, Y.Yamamoto, A.Yoshise: "Global Optimization Method for Solving Mathematical Programs with Linear Complementarity Constraints"Journal of Optimization Theory and Applications. 124(To appear). (2005)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] A.Yoshise: "A homogeneous model for PO and P* nonlinear complementarity problems"The Institute of Statistics and Mathernatics Co-operative Report, Optimization : Modeling and Algorithms. 16. 200-220 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Iwata, M.Shigeno: "Conjugate Scaling Technique for Feanchel-Type Duality in Discrete Convex Optimization"SIAM Journal on Optimization. 13. 204-211 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] J.Gotoh, N.Thoai, Y.Yamamoto: "Global Optimization Method for Solving the Minimum Maximal Flow Problem"Optimization Method and Software. 18. 395-415 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 反町宏明, 吉瀬章子: "サポートベクターマシンにおけるカーネル行列の最適化"統計数理研究所共同研究レポート「最適化-モデリングとアルゴリズム」. (印刷予定). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] N.Thoai, Y.Yamamoto, A.Yoshise: "Global Optimization Method for Solving Mathematical Programs with Linear Complementarity Constraints"Journal of Optimization Theory and Applications. (印刷予定).

    • Related Report
      2003 Annual Research Report
  • [Publications] 吉瀬章子: "A homogeneous model for PO and P* nonlinear complementarity problems"統計数理研究所共同研究レポート「最適化-モデリングとアルゴリズム」. 16. 200-220 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Iwata, M.Shigeno: "Conjugate Scaling Technique for Feanchel-Type Duality in Discrete Convex Optimization"SIAM Journal on Optimization. 13. 204-211 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] J.Gotoh, N.Thoai, Y.Yamamoto: "Global Optimization Method for Solving the Minimum Maximal Flow Problem"Optimization Method and Software. 18. 395-415 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Keisuke Hotta, Akiko Yoshise: "A Complexity Bound of a Predictor-Corrector Smoothing Method Using CHKS-functions for Monotone LCP"Computational Optimization and Applications. 22. 351-367 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Akiko Yoshise: "A homogeneous model for Po and P* nonlinear complementarity problem"Optimization -Modeling and Algorithms-. (to appear).

    • Related Report
      2002 Annual Research Report
  • [Publications] Mika Sato-Ilic: "Dynamic fuzzy clustering using fuzzy cluster loading"Intelligent Engineering Systems Through Artificial Neural Networks. 12. 309-314 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Maiko Shigeno: "Maximum network flows with concave gains"The 3rd Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications. 204-213 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] K. Hotta, A. Yoshise: "A complexity bound of a predictor corrector smoothing method using CHKS-functions for monotone linear complementarity problems"Computational Optimization and Applications. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] Yoshitsugu Yamamoto: "Optimization over the efficient set - Overview"Journal of Global Optimization. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] Maiko Shigeno: "Minimax Inverse Problems of Minimum Cuts"Networks. 39. 7-14 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] M. Sato-Ilic: "On Clustering based on Homogeneity"Joint 9th IFSA World Congress and 20th NAFIPS International Conference. 2505-2510 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Takahito Kuno: "A finite branch-and-bound algorithm for linear multiplicative programming"Computational Optimization and Applications. 20. 119-135 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kazutoshi Ando: "K-submodular functions and convexity of their Lovasz extention"Discrete Applied Mathematics. 122(to appear). 1-12 (2002)

    • Related Report
      2001 Annual Research Report

URL: 

Published: 2001-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi