解无约束优化问题的一个新的带线搜索的信赖域算法  

A TRUST REGION ALGORITHM WITH NEW LINE SEARCH FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEMS

作　　者：刘景辉[1] 马昌凤[1] 陈争[2] 

机构地区：[1]福建师范大学数学与计算机科学学院,福州350007 [2]福建江夏学院信息系,福州350108

出　　处：《计算数学》2012年第3期275-284,共10页Mathematica Numerica Sinica

基　　金：国家自然科学基金(11071041)资助项目

摘　　要：在传统信赖域方法的基础上,提出了求解无约束最优化问题的一个新的带线搜索的信赖域算法.该算法采用大步长Armijo线搜索技术获得达代步长,克服了每次迭代求解信赖域子问题时计算量较大的缺点,因而适用于求解大型的优化问题.在适当的条件下,我们证明了算法的全局收敛性.数值实验结果表明本文所提出的算法是有效的.Based on the traditional trust region method, a trust region algontnm with new nne search is proposed for solving unconstrained optimization problems. The stepsize is ob- tained making use of larger Armijo line search rule. The proposed algorithm overcomes the shortcomings of large amount of calculation when solving the subproblem at each iteration, therefore, it is more attractive for large scale optimization problems. The global convergence of the algorithm is proved under suitable conditions. Some numerical results are reported, which shows that our algorithm is quite effective.

关 键 词：无约束优化问题 信赖域方法 大步长Armijo线搜索 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]