パラメトリック単体法による非凸型関数の大域的最小化 Global minimization of nonconvex functions by parametric simplex algorithm

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Recently, a remarkable progress has been made in the field of the global minimization of nonconvex functions over a polytope. The purpose of this article is to survey one of the most successful approaches in this field, namely parametric programming approaches to quasilinear nonconvex minimization problems. The problems to be discussed are: linear multiplicative programming problems, i. e., the minimization of the product of two affine functions; minimization of the sum of two linear fractional functions; minimization of concave quadratic functions and bilinear programming problems. It will be shown that a global minimum of a fairly large scale problems can be obtained efficiently by applying parametric simplex algorithms. Further, it will be shown that a convex multiplicative programming problems, i. e., the minimization of the product of two convex functions, can be solved by parametrizatioh and branch and bound techniques.

収録刊行物

  • 応用数理

    応用数理 1(1), 36-50, 1991

    一般社団法人 日本応用数理学会

各種コード

  • NII論文ID(NAID)
    110007390291
  • 本文言語コード
    JPN
  • データ提供元
    NII-ELS  J-STAGE 
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