Armijo搜索下求解无约束优化问题的扰动BFGS方法

数学理论与应用 ›› 2018, Vol. 38 ›› Issue (3-4): 85-92.

Armijo搜索下求解无约束优化问题的扰动BFGS方法

严娇娇

长沙理工大学数学与统计学院

出版日期:2018-12-30 发布日期:2020-09-21

The Perturbed BFGS Method for the Unconstrained Optimization with the Armijo Line Search

Online:2018-12-30 Published:2020-09-21

摘要/Abstract

摘要： 文献[3]提出了一种求解无约束优化问题的扰动BFGS方法,并在Wolfe搜索下证明了其全局收敛性.本文证明了该扰动BFGS方法在较弱的Armijo线性搜索下求解非凸问题也具有全局收敛性.数值结果表明在 Armijo搜索下该方法也具有较好的数值效果.

关键词: BGFS方法, Armijo线性搜索, 全局收敛性

Abstract: A perturbed BFGS method was proposed in[3]to solve the unconstrained optimization and was proved to be globally convergent when the Wolfe line search is used.In this paper,we show that the perturbed BFGS method also possesses global convergence for nonconvex problems with the relatively weaker Armijo line search.Numerical results show that this method with the Armijo search is also promising.

Key words: BGFS method, Armijo linear search , Global convergence

严娇娇. Armijo搜索下求解无约束优化问题的扰动BFGS方法[J]. 数学理论与应用, 2018, 38(3-4): 85-92.

Yan Jiaojiao. The Perturbed BFGS Method for the Unconstrained Optimization with the Armijo Line Search[J]. Mathematical Theory and Applications, 2018, 38(3-4): 85-92.