带有线搜索的新的非单调自适应信赖域算法  

A New Nonmonotonic Self-adaptive Trust Region Algorithm with Line Search

作　　者：杨扬[1] 孙文瑜[2] 

机构地区：[1]徐州工程学院数学与物理科学学院,徐州221008 [2]南京师范大学数学与计算机科学学院,南京210097

出　　处：《工程数学学报》2007年第5期788-794,共7页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China (10231060);the Special Research Fund of Doctoral Program of Higher Education of China (20040319003);the Graduates' Creative Project of Jiangsu Province,China.

摘　　要：本文给出了一种新的信赖域算法。该算法以变化的速率来调整信赖域半径的大小。在由信赖域子问题产生的试探步不被接受的情况下,新算法采用线搜索的方法得到下一个迭代点。同时算法采用非单调的技术来加速算法的收敛效果。文中给出了新算法的全局收敛性分析和数值试验的结果。We propose a new trust region algorithm which the trust region radius is updated at a variable rate. Moreover, the new algorithm performs a backtracking line search from the failed point instead of resolving the trust region subproblem. A nonmonotonic criterion is also used to speed up the convergence. We establish the global convergence of the new algorithm. Numerical results are also presented.

关 键 词：无约束优化 信赖域 线搜索 非单调 全局收敛性 

分 类 号：O221.2[理学—运筹学与控制论]