摘要
宇和濮在文[Yu Z S,Pu D G.A new nonmonotone line search technique for unconstrained optimization[J].J Comput Appl Math,2008,219:134-144]中提出了一种非单调的线搜索算法解无约束优化问题.和他们的工作不同,当优化问题非凸时,本文给出了一种非单调滤子曲率线搜索算法.通过使用海森矩阵的负曲率信息,算法产生的迭代序列被证明收敛于一个满足二阶充分性条件的点.在不需要假设极限点存在的情况下,证明了算法具有整体收敛性,而且分析了该算法的收敛速率.数值试验表明算法的有效性.
Yu and Pu [Yu Z S, Pu D G. A new nonmonotone line search technique for unconstrained optimization [J]. J Comput Appl Math, 2008, 219：134-144] introduced a non- monotone line search algorithm for unconstrained optimization. Different from their work, the authors propose a nonmonotone filter curvilinear line search algorithm when a problem may be nonconvex. By using the negative curvature information of the Hessian, the gener- ated sequence is shown to converge to stationary points that satisfy second-order optimality conditions. Global convergence is established even without requiring a priori the existence of a limit point. Moreover, the authors analyze the convergence rate of the new algorithm. The numerical experiments are reported to show the effectiveness of the DroDosed algorithm.
出处
《数学年刊（A辑）》
CSCD
北大核心
2017年第4期391-404,共14页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.11201304
No.11371253)
上海市自然科学基金
上海立信会计金融学院统计学一级学科项目的资助
关键词
非凸优化
非单调
曲率线搜索
滤子
收敛性
Nonconvex optimization, Nonmonotone, Curvilinear line search, Filter, Convergence
