带有固定步长的非单调信赖域方法  

A Nonmonotone Trust Region Method with Fixed Stepsize

作　　者：莫降涛[1] 刘春燕[1] 颜世翠[1] 

机构地区：[1]广西大学数学与信息科学学院,广西壮族自治区南宁市530004

出　　处：《曲阜师范大学学报（自然科学版）》2006年第3期30-34,共5页Journal of Qufu Normal University(Natural Science)

基　　金：广西自然科学基金(桂科自0542043)

摘　　要：该文提出一种新的非单调信赖域方法.当试探步不能被接受时,算法沿着试探步的方向求得下一个迭代点,其中步长利用固定公式计算.这种方法既避免了重复求解信赖域子问题,又减少了线搜索方法计算函数值的次数.该文采用的非单调策略是基于张洪超和Hanger(2004)提出的非单调线搜索技术.在适当的条件下,证明了算法的全局收敛性及超线性收敛性.最后给出了初步的数值实验结果.In this paper, a new nonmonotone trust region method is presented. If the trial step is rejected, the method finds a new iteration point along the trial step and the stepsize is computed by a fixed formula. The method not only avoids resolving the subproblem repeatedly but also reduces the numbers of computing function values in the line search algorithm. The nonmonotone technique applied to the method is based on the nonmonotone line search technique proposed by Zhang and Hanger（2004）. The global convergence and superlinear convergence results of algorithm are preserved under suitable conditions. Some preliminary numerical results are given.

关 键 词：固定步长 非单调线搜索 非单调信赖域方法 全局收敛性 超线性收敛性 

分 类 号：O221.2[理学—运筹学与控制论]