一个采用组合信赖域与二阶线搜索技术的新的非单调大规模最优化方法  

A NEW NONMONOTONE OPTIMIZATION METHOD WITH TRUST REGION AND SECOND ORDER LINE SEARCH

作　　者：陈艳男[1,2] 孙文瑜[1] 

机构地区：[1]南京师范大学数学科学学院,南京210046 [2]南京林业大学理学院应用数学系,南京210037

出　　处：《高等学校计算数学学报》2010年第4期369-386,共18页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(No.10871098);江苏省自然科学基金(No.BK2009397)资助项目

摘　　要：本文考虑求解大规模无约束最优化问题 minf（x）,x∈R^n,其中f：R^n→R是二阶连续可微的实值目标函数,n是一个比较大的正整数.在求解问题（1.1）时,通常的迭代法产生一个迭代点列x0,x1,x2,…,A new method combining trust region and second order line search for large scale unconstrained optimization is presented in this paper.The trust region subproblem is solved inexactly,and the solution only satisfies the Cauchy descent condition which may not satisfy the gradient-related sufficient descent condition.A second order line search technique is employed for dealing with this problem,and the step length of the second order line search is bounded above and below away from zero.The new method with average non-monotone technique is proposed,and its convergence is proved.Preliminary numerical results on a set of large scale CUTEr test problems are reported.These results show the efficiency and prominence of the algorithm.

关 键 词：二阶连续可微 最优化方法 搜索技术 非单调 信赖域 无约束最优化问题 求解问题 目标函数 

分 类 号：O221.2[理学—运筹学与控制论]