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A Research on Practical Algorithms for Geometrical Optimization Problems with Nonconvex Structure

Research Project

Project/Area Number 05650061
Research Category

Grant-in-Aid for General Scientific Research (C)

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

Principal Investigator

KUNO Takahito  Institute of Information Sciences and Electronics, University of Tsukuba Associate Professor, 電子・情報光学系, 助教授 (00205113)

Project Period (FY) 1993 – 1994
Project Status Completed (Fiscal Year 1994)
Budget Amount *help
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1994: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1993: ¥700,000 (Direct Cost: ¥700,000)
KeywordsMathematical Programming / Global optimization / Nonconvex function / Computational Geometry / Algorithm
Research Abstract

In this research, we studied some practical algorithme for solving certain classes of geometrical optimization problems with nonconvex structure. We applied global optimization techniques to the problems in the plane and constructed some algorithms for obtaining a globally optimal solution. A few of the results are as follows :
1.Globally optimization of rank-two reverse convex programs : We proposed an algorithm for solving reverse convex program which contains a quasiconcave constraint function defined by two linearly independent n-dimensional vectors. The computational experiments indicated that the algorithm can generate globally optimal solutions very efficiently compared with any existing algorithms.
2.Globally minimization of rank-two saddle functions on a polytope : We proposed an algorithm for minimizing a composite function of a two-dimensional saddle function and n-dimensional affine functions. The computational experiments indicated that the algorithm solves fairly large scale problems.
In addition to the above problems, we studied a class of nonconvex network optimization problems. To solve the problems efficiently, we used computational geometry as some procedures of the algorithm. As a result, we obtained the following :
3.Globally optimization of production-transportation problems : We proposed a pseudopolynomial-time algorithm for solving a class of production-transportation problem.
All the above mentioned algorithms decompose a given problem into several convex subproblems. This solution strategy can also be applied to many other classes of optimization problems.

Report

(3 results)
  • 1994 Annual Research Report   Final Research Report Summary
  • 1993 Annual Research Report
  • Research Products

    (19 results)

All Other

All Publications (19 results)

  • [Publications] Takahito Kuno: "A parametric simplex algorithm for solving a class of rank-two reverse convex programs" ISE Report, Inst.of lnformation Sciences & Electronics,Univ. of Tsukuba. 93-103. 1-21 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Takahito Kuno: "A practical algorithm for minimizing a rank-two saddle function on a polytope" Journal of the Operations Research Society of Japan. (掲載予定)(印刷中). (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Takahito Kuno: "Parametric methods for solving low-rank reverse convex programs" 第6回RAMP(数理計画法研究会)シンポジウム論文集. 45-56 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Takahito Kuno: "Gonvex programs with an additional constraint on the product of several convex functions" European Journal of Operational Research. 77. 314-324 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Takahito Kuno: "A decomposition algorithm for solving certain classes of production-transportation problems" ISE Report, Inst. of Information Sciences & Electronics, Univ. of Tsukuba. 94-113. 1-12 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Hiroshi Konno: ""Multiplicative programming problems"in Handbook of Global Optimization" Kluwer Accademic Publishers, 37 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Kuno: ""A parametric simplex algorithm for solving a class of rank-two reverse convex programs, "" ISE Report 93-103(Inst.of Information Sciences & Electronics, Univ.of Tsukuba). (1933)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Kuno: ""A practical algorithm for minimizing a rank-two saddle function on a polytope, "" to appear in Journal of the Operations Research Society of Japan.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Kuno: ""Parametric methods for solving low-rank reverse convex programs, "" Proceedings of the 6th RAMP Symposium. (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Kuno: ""Gonvex programs with an additional constraint on the product of several convex functions, "" European Journal of Operational Research. 77. 314-324 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Kuno: ""A decomposition algorithm for solving certain classes of production-transportation problems, "" ISE Report 94-113 (Inst.of Information Sciences & Electronics, Univ.of Tsukuba). (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] H.Konno: ""Multiplicative programming problems" in Handbook of Global Optimizationproblems" (Kluwer Accademic Publishers). 369-405 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Takahito Kuno: "A practical algorithm for minimizing a rank-two saddle function on a polytope" Journal of the Operations Research Society of Japan に掲載予定. (印刷中). (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] Takahito Kuno: "Parametric methods for solving low-rank reverse convex programs" 第6回RAMP(数理計画法研究会)シンポジウム論文集. (印刷中). (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Takahito Kuno: "Gonvex programs with an additional constraint on the product of several convex functions" European Journal of Operational Research. 77. 314-324 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Takahito Kuno: "A decomposition algorithm for solving certain classes of production-transportation problems" ISE Report.Inst.of Information Sciences & Electronics,Univ.of Tsukuba22GD04:94-113. (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Takahito Kuno: "A parametric simplex algorithm for solving a class of rank-two reverse convex programs" ISE Report,Inst.of Information Sciences & Electronics,Univ.of Tsukuba. 93-103. 1-21 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Takahito Kuno: "An efficient algorithm for minizing a rank-two saddle function on a polytope" ISE Report,Inst.of Information Sciences & Electronics,Univ.of Tsukuba. 94-105. 1-14 (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] Hiroshi Konno: "Multiplicative programming" Kluwer Accademic Publishers(Handbook of Global Optimizationに掲載予定),

    • Related Report
      1993 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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