Chinese Quarterly Journal of Mathematics ›› 2011, Vol. 26 ›› Issue (2): 285-289.

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Nonmonotonic Trust Region Algorithm via the Conjugate Gradient Path for Unconstrained Generalized Geometric Programming 

  

  1. 1. School of Management, University of Shanghai for Science and Technology2. College of Mathematics and Information Science, Henan Polytechnic University
  • Received:2008-03-14 Online:2011-06-30 Published:2023-05-05
  • About author:DANG Ya-zheng(1973-), female, native of Xuchang, Henan, a lecturer of Henan Polytechnic University, engages in optimization; JING Shu-jie(1965-), male, native of Changyun, Henan, an associate professor of Henan Polytechnic University, engages in optimization; LI Yu(1969-), female, native of Kaifeng, Henan, an associate professor of Henan University, engages in intelligent optimization.
  • Supported by:
    Supported by the National Science Foundation of China(10671126); Supported by the Shanghai Municipal Government Project(S30501); Supported by the Innovation Fund Project for Graduate Student of Shanghai(JWCXSL1001); Supported by the Youth Foundation of Henan Polytechnic University(Q20093); Supported by the Applied Mathematics Provinciallevel Key Discipline of Henan Province; Supported by Operational Research and Control Theory Key Discipline of Henan Polytechnic University;

Abstract: In this paper, on the basis of making full use of the characteristics of unconstrained generalized geometric programming(GGP), we establish a nonmonotonic trust region algorithm via the conjugate path for solving unconstrained GGP problem. A new type of condensation problem is presented, then a particular conjugate path is constructed for the problem, along which we get the approximate solution of the problem by nonmonotonic trust region algorithm, and further prove that the algorithm has global convergence and quadratic convergence properties. 

Key words: generalized geometric programming, condensation conjugate path, trust region

CLC Number: