基于简单二次函数模型的滤子非单调信赖域算法

J4 ›› 2012, Vol. 47 ›› Issue (5): 108-114.

基于简单二次函数模型的滤子非单调信赖域算法

冯琳^1,2,段复建¹,和文龙¹

1. 桂林电子科技大学数学与计算科学学院, 广西桂林 541004;
2. 安徽科技学院理学院, 安徽凤阳 233100

收稿日期:2011-08-09 出版日期:2012-05-20 发布日期:2012-06-01
作者简介:冯琳(1973- ),女,硕士研究生,讲师,研究方向为最优化理论与方法.Email:fenglin750825@126.com
基金资助:
国家自然科学基金资助项目(11061011);广西自然科学基金资助项目(2011GXNSFA018138)

A filter non-monotone trust region algorithm with a simple quadratic model

FENG Lin^1,2, DUAN Fu-jian¹, HE Wen-long¹

1. School of Mathematics and Computational Science, Guilin University of
Electronic Technology, Guilin 541004, Guangxi, China;
2.School of Science, Anhui Science and Technology University, Fengyang 233100, Anhui, China

Received:2011-08-09 Online:2012-05-20 Published:2012-06-01

摘要/Abstract

摘要：

对无约束最优化问题提出了一个基于简单二次函数模型的非单调滤子信赖域算法。算法在信赖域试探步不被接受时,采用滤子技术,增大试探步被接受的可能性;如果此试探步也不能被滤子集接受,则用固定的公式取搜索方向,并沿此搜索方向进行非单调Wolfe线搜索得到步长,从而产生新的迭代点。该算法不需要重解子问题,减少了计算量。在较少的条件下,证明了算法的全局收敛性。初步的数值试验表明了算法的有效性。

关键词: 无约束最优化;非单调信赖域算法;滤子;简单二次函数模型;全局收敛性

Abstract:

A filter non-monotone trust region algorithm based on a simple quadratic model is proposed for unconstrained optimization problems. A filter technique is employed into the method, which makes the trial point of the trust region sub-problem be taken more often. If the trial step is also rejected by the filter set, a search direction is obtained by a fixed formula and a step size is obtained by the non-monotonic Wolfe line search, and thus a new iterative point is achieved. The algorithm does not resolve the trust region sub-problem, so the amount of computation is reduced.The global convergence of this new method is presented under fewer conditions. Preliminary numerical experiments show that the new method is effective.

Key words: unconstrained optimization; non-monotonic trust region algorithm; filter; simple quadratic model; global convergence

冯琳1,2,段复建1,和文龙1. 基于简单二次函数模型的滤子非单调信赖域算法[J]. J4, 2012, 47(5): 108-114.

FENG Lin1,2, DUAN Fu-jian1, HE Wen-long1. A filter non-monotone trust region algorithm with a simple quadratic model[J]. J4, 2012, 47(5): 108-114.

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