A NEW ADAPTIVE TRUST REGION ALGORITHM FOR OPTIMIZATION PROBLEMS

doi:10.1016/S0252-9602(18)30762-8

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (2): 479-496.doi: 10.1016/S0252-9602(18)30762-8

A NEW ADAPTIVE TRUST REGION ALGORITHM FOR OPTIMIZATION PROBLEMS

盛洲, 袁功林, 崔曾如

College of Mathematics and Information Science, Guangxi University, Nanning 530004, China

收稿日期:2016-07-09 修回日期:2016-10-13 出版日期:2018-04-25 发布日期:2018-04-25
通讯作者: Gonglin YUAN E-mail:glyuan@gxu.edu.cn
作者简介:Zhou SHENG,E-mail:szhou03@live.com;Zengru CUI,E-mail:cuizengru@126.com
基金资助:
Supported by the National Natural Science Foundation of China (11661009), the Guangxi Science Fund for Distinguished Young Scholars (2015GXNSFGA139001), the Guangxi Natural Science Key Fund (2017GXNSFDA198046), and the Basic Ability Promotion Project of Guangxi Young and Middle-Aged Teachers (2017KY0019).

A NEW ADAPTIVE TRUST REGION ALGORITHM FOR OPTIMIZATION PROBLEMS

Zhou SHENG, Gonglin YUAN, Zengru CUI

College of Mathematics and Information Science, Guangxi University, Nanning 530004, China

Received:2016-07-09 Revised:2016-10-13 Online:2018-04-25 Published:2018-04-25
Contact: Gonglin YUAN E-mail:glyuan@gxu.edu.cn
Supported by:
Supported by the National Natural Science Foundation of China (11661009), the Guangxi Science Fund for Distinguished Young Scholars (2015GXNSFGA139001), the Guangxi Natural Science Key Fund (2017GXNSFDA198046), and the Basic Ability Promotion Project of Guangxi Young and Middle-Aged Teachers (2017KY0019).

摘要/Abstract

摘要：

It is well known that trust region methods are very effective for optimization problems. In this article, a new adaptive trust region method is presented for solving unconstrained optimization problems. The proposed method combines a modified secant equation with the BFGS updated formula and an adaptive trust region radius, where the new trust region radius makes use of not only the function information but also the gradient information. Under suitable conditions, global convergence is proved, and we demonstrate the local superlinear convergence of the proposed method. The numerical results indicate that the proposed method is very efficient.

关键词: Optimization, trust region method, global convergence, local convergence

Abstract:

Key words: Optimization, trust region method, global convergence, local convergence

盛洲, 袁功林, 崔曾如. A NEW ADAPTIVE TRUST REGION ALGORITHM FOR OPTIMIZATION PROBLEMS[J]. 数学物理学报(英文版), 2018, 38(2): 479-496.

Zhou SHENG, Gonglin YUAN, Zengru CUI. A NEW ADAPTIVE TRUST REGION ALGORITHM FOR OPTIMIZATION PROBLEMS[J]. Acta mathematica scientia,Series B, 2018, 38(2): 479-496.

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A NEW ADAPTIVE TRUST REGION ALGORITHM FOR OPTIMIZATION PROBLEMS

A NEW ADAPTIVE TRUST REGION ALGORITHM FOR OPTIMIZATION PROBLEMS

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