基于混合非单调下降条件的直接搜索方法  

A DIRECT SEARCH METHOD BASED ON THE MIXED NONMONOTONE DECREASE CONDITION

作　　者：刘群锋[1] 曾金平[1] 张忠志[1] 程万友[1] 

机构地区：[1]东莞理工学院,计算机学院,广东东莞523808

出　　处：《计算数学》2015年第2期213-224,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金(#11271069);教育部人文社会科学基金(#13YJC630095)资助

摘　　要：基于混合非单调下降条件提出了一种网格步长的更新策略.这种策略要求发现强最小网格单元框时网格步长快速下降,而发现其他拟最小网格单元框时缓慢下降.这种混合非单调下降策略可以避免网格步长下降太快,又能够比单纯非单调下降条件更好地保证直接搜索算法的收敛性.基于这一策略,本文提出一个直接搜索算法,并证明了该算法的全局收敛性.数值试验表明,本文提出的算法是很有竞争力的直接搜索算法.In this paper, a new strategy for updating the grid size is proposed based on the mixed nonmonotone decrease condition. Such strategy let the grid size decrease rapidly when a strongly minimal frame is found but decrease slowly when other quasi-minimal frame is found. It is shown in this paper that such strategy can avoid the grid size decreasing too fast, and moreover, it needs weaker convergence conditions than the pure nonmonotone decrease strategy. A direct search method is then proposed based on such strategy, and its global convergence is proved. Numerical results show that the proposed method is competitive.

关 键 词：直接搜索 混合非单调下降 共轭梯度 全局收敛 

分 类 号：O224[理学—运筹学与控制论]