非线性比式和问题的全局优化算法

数学季刊 ›› 2008, Vol. 23 ›› Issue (4): 499-505.

非线性比式和问题的全局优化算法

1. Department of Mathematics,Henan Institute of Science and Technology,Xinxiang 453003,China2. College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China

收稿日期:2006-03-25 出版日期:2008-12-30 发布日期:2023-09-14
作者简介:JIAO Hong-wei(1978-), male, native of Zhoukou, Henan, a lecturer of Henan Institute of Science and Technology, engage in optimization theory and algorithm, global optimization.
基金资助:
Supported by the National Natural Science Foundation of China(10671057)； Supported by the Natural Science Foundation of Henan Institute of Science and Technology(06054)；

Global Optimization Algorithm for Nonlinear Sum of Ratios Problems

1. Department of Mathematics,Henan Institute of Science and Technology,Xinxiang 453003,China2. College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China

Received:2006-03-25 Online:2008-12-30 Published:2023-09-14
About author:JIAO Hong-wei(1978-), male, native of Zhoukou, Henan, a lecturer of Henan Institute of Science and Technology, engage in optimization theory and algorithm, global optimization.
Supported by:
Supported by the National Natural Science Foundation of China(10671057)； Supported by the Natural Science Foundation of Henan Institute of Science and Technology(06054)；

摘要/Abstract

摘要： In this paper,a global optimization algorithm is proposed for nonlinear sum of ratios problem(P).The algorithm works by globally solving problem(P1) that is equivalent to problem(P),by utilizing linearization technique a linear relaxation programming of the (P1) is then obtained.The proposed algorithm is convergent to the global minimum of(P1) through the successive refinement of linear relaxation of the feasible region of objective function and solutions of a series of linear relaxation programming.Numerical results indicate that the proposed algorithm is feasible and can be used to globally solve nonlinear sum of ratios problems(P).

关键词: global optimization, nonlinear sum of ratios, linearization technique

Abstract: In this paper,a global optimization algorithm is proposed for nonlinear sum of ratios problem(P).The algorithm works by globally solving problem(P1) that is equivalent to problem(P),by utilizing linearization technique a linear relaxation programming of the (P1) is then obtained.The proposed algorithm is convergent to the global minimum of(P1) through the successive refinement of linear relaxation of the feasible region of objective function and solutions of a series of linear relaxation programming.Numerical results indicate that the proposed algorithm is feasible and can be used to globally solve nonlinear sum of ratios problems(P).

Key words: global optimization, nonlinear sum of ratios, linearization technique

中图分类号:

O224

焦红伟, 郭运瑞, 陈永强. 非线性比式和问题的全局优化算法[J]. 数学季刊, 2008, 23(4): 499-505.

JIAO Hong-wei, GUO Yun-rui, CHEN Yong-qiang. Global Optimization Algorithm for Nonlinear Sum of Ratios Problems[J]. Chinese Quarterly Journal of Mathematics, 2008, 23(4): 499-505.

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