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New Methods for Distance Geometry Problems

Research Project

Project/Area Number 13650063
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionTokyo Institute of Technology

Principal Investigator

YAJIMA Yasutoshi  Tokyo Institute of Technology, Graduate School of Decision Science and Technology, Associate Professor, 大学院・社会理工学研究科, 助教授 (80231645)

Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2002: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2001: ¥2,300,000 (Direct Cost: ¥2,300,000)
KeywordsDistance Geometry / Molecular Conformation / Positive Semidefinite Programming / 大域的最適化 / 非凸2次計画問題 / 半正定値計画 / 大域的的最適化
Research Abstract

We consider distance geometry problems for determining $r$--dimensional coordinates of $n$ points from a given set of the distances between the points. This problem is a fundamental problem in molecular biology for finding the structure of proteins from NMR (Nuclear Magnetic Resonance) data.
We formulate the problem as the minimization of an error function defined by the sum of the absolute differences, which is a typical nonconvex optimization problem. We show that this problem can be reduced into a concave quadratic minimization problem. We propose positive semidefinite relaxations as well as local search procedures for this problem. Our numerical results show that we can generate acceptable solutions of the problem with up to 800 points.

Report

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

    (8 results)

All Other

All Publications (8 results)

  • [Publications] Yajima, Yasutoshi: "Positive Semidefinite Relaxations for Distance Geometry Problems"JJIAM. 19. 87-112 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Yajima, Yasutoshi: "Cuts and Semidefinite Relaxations for Nonconvex Quadratic Problems"Generalized convexity and generalized monotonicity Lecture notes in economics and mathematical systems, Springer. 48-70 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Yajima, Yasutoshi: "Positive Semidefinite Relaxations for Distance Geometry Problems"JJIAM. 19. 87-112 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Yajima, Yasutoshi, P. M. Pardalos, M. V. Ramana: "Cuts and Semidefinite Relaxations for Nonconvex Quadratic Problems, Generalized convexity and generalized monotonicity , Lecture notes in economics and mathematical systems"Springer. 48-70 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Kou, Y.Yajima: "Approximate Reducts of an Information System"Technical Report. 2002・7. 1-9 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Yajima: "Linear Programming Approaches for Multicategory Support Vector Machines"Technical Report. 2002・6. 1-23 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Yajima, H.Ohi, M.Mori: "Extracting Feature Subspace for Kernel Based Support Vector Machies"OR学会春季研究発表会. 18-19 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Yajima: "Positive Semidefinite Relaxations for Distance Geometry Problems"JJIMA. 19・1. 87-112 (2002)

    • Related Report
      2002 Annual Research Report

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

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