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A unified approach to nonconvex programming problems using branch-and-bound algorithms

Research Project

Project/Area Number 13680505
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 社会システム工学
Research InstitutionUniversity of Tsukuba

Principal Investigator

KUNO Takahito  Univesity of Tsukuba, Institute of Information Sciences and Electronics, Associate Professor, 電子・情報工学系, 助教授 (00205113)

Co-Investigator(Kenkyū-buntansha) YOSHISE Akiko  Univesity of Tsukuba, Institute of Policy and Planning Sciences, Associate Professor, 社会工学系, 助教授 (50234472)
Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2002: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2001: ¥2,100,000 (Direct Cost: ¥2,100,000)
KeywordsGlobal optimization / nonconvex program / branch-and-bound method / mathematical programming / algorithm
Research Abstract

We made a study mainly on three classes of nonconvex optimization problems, each of which is abundant in applications to real-world social systems :
(1) In almost every optimization problem, both objective and constraint functions can be written as the difference of two convex functions. Using this property, the problem can be trans-formed into a convex minimization problem with an additional reverse convex constraint. We proposed three branch-and-bound algorithms for solving this kind of nonconvex optimization problems. We showed that each algorithm generates a globally optimal solution in finite iterations if the reverse convex constraint function is separable.
(2) The sum-of-ratios problem is a problem, of minimizing a sum of linear rations over a convex set, and is known to be intractable. We devised an inexpensive procedure for computing a tignt lower bound on the optical value. We incorporated it into a branch-and-bound algorithm and succeeded in solving the problem much faster than the existing algorithms.
(3) Many of chemical process design problems can be formulated as optimization problems but highly nonconvex ones, say mixed-integer nonlinear programming problems. To solve this kind of problems, we proposed a hybrid algorithm of brand-and-bound and revised general benders decomposition methods. We then proved that the algorithm certainly converges to globally optimal solutions for some typical chemical process design problems.
Each of the proposed algorithms is based on the idea of branch and bound. To execute the bounding operations efficiently, we also studied an interior-point algorithm for solving relaxed problems.

Report

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

    (11 results)

All Other

All Publications (11 results)

  • [Publications] T.Kuno, J.Shi: "Linear programs with an additional separable concave constraint"ISE Technical Report. 181. 1-25 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Kuno: "A finite algorithm for separable reverse convex programs"ICOTA2001 Proceedings. 2. 608-609 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Zhu, T.Kuno: "Global optimization of nonconvex MILP by a hybrid brance-and-bound and revised general Benders decomposition approach"Industrial and Engineering Chemistry Research. 42. 528-539 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Yoshise: "A homogeneous model for Po and P* nonlinear complementarity problems"ISM Technical Report. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Kuno and J. Shi: "Linear programs with an additional separable concave constraint"ISE Technical Report. 181. 1-25 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Kuno: "A finite algorithm for separable reverse convex programs"ICOTA2001 Proceedings. 2. 608-609 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y. Zhu and T. Kuno: "Global optimization, of nonconvex MINLP by a hybrid branch-and-bound and revised gneral Benders decomposition, approach"Industrial and Engineering Chemistry Research. 42. 528-539 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y. Yoshise: "A homogeneous model for P_0 and P_* nonlinear complementarity problems"ISM Technical Report. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Yashan Zhu, Takahito Kuno: "Global Optimization of Nonconvex MILP by a Hybrid Branch-and-Bound and Revised General Benders Decomposition"Industrial and Engineering Chemistry Research. 42. 528-539 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Takahito Kuno: "Linear Programs with an Additional Separable Concave Constraint"ISE Technical Report. 01・181. 1-27 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Takahito Kuno: "A finite Algorithm for Separable Reverse Convex Programs"ICOTA2001 Proceedings. 2. 608-609 (2001)

    • Related Report
      2001 Annual Research Report

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

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