广义几何规划的压缩共轭梯度路径非单调信赖域算法

数学季刊 ›› 2011, Vol. 26 ›› Issue (2): 285-289.

广义几何规划的压缩共轭梯度路径非单调信赖域算法

1. School of Management, University of Shanghai for Science and Technology2. College of Mathematics and Information Science, Henan Polytechnic University

收稿日期:2008-03-14 出版日期:2011-06-30 发布日期:2023-05-05
作者简介: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.
基金资助:
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；

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

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；

摘要/Abstract

摘要： 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.

关键词: generalized geometric programming, condensation conjugate path, trust region

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

中图分类号:

O221

党亚峥, 景书杰, 李煜. 广义几何规划的压缩共轭梯度路径非单调信赖域算法[J]. 数学季刊, 2011, 26(2): 285-289.

DANG Ya-zheng, JING Shu-jie, LI Yu. Nonmonotonic Trust Region Algorithm via the Conjugate Gradient Path for Unconstrained Generalized Geometric Programming [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(2): 285-289.

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