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1994 Fiscal Year Final Research Report Summary

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
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.

  • Research Products

    (12 results)

All Other

All Publications (12 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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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

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Published: 1996-04-15  

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