一类带线搜索的非单调自适应信赖域算法  

A Nonmonotonic Self-adaptive Trust Region Algorithm with Line Search

作　　者：李红[1] 焦宝聪[1] 

机构地区：[1]首都师范大学数学科学学院,北京100037

出　　处：《首都师范大学学报（自然科学版）》2008年第2期1-5,共5页Journal of Capital Normal University：Natural Science Edition

基　　金：国家自然科学基金(60472071);北京市教委科研基金(KM200510028019)

摘　　要：对无约束优化问题提出了一类新的非单调信赖域方法,与通常非单调信赖域方法不同,当试验步失败时并不重解信赖域子问题,而采用非单调线搜索.新算法利用一个R-函数以变化的速率来调整信赖域半径的大小,而不是简单的扩大或缩小一个常数倍.文中在一定的条件下证明了算法的收敛性,并且给出了相应的数值实验结果.A new nonmonotonic trust region algorithm for unconstrained optimization is proposed. Unlike traditional nonmonotonic trust region methods, our algorithm does not resove the subproblem if the trial step is not successful, but instead performs a nonmonotonic line search from the failed point. The trust region radius is updated at a variable rate by R-function, rather than by simply enlarging or reducing the original trust region radius at a constant rate. The convergence of the new algorithm is proved and numerical results are also presented.

关 键 词：非单调线搜索 自适应 信赖域方法 无约束最优化 

分 类 号：O186.16[理学—数学]