无约束优化的自适应信赖域方法(英文)  

A Self-adaptive Trust Region Method For Unconstrained Optimization

作　　者：章祥荪[1] 陈中文[2] 张菊亮[1] 

机构地区：[1]中科院数学与系统科学研究院,北京100080 [2]苏州大学数学系,苏州215006

出　　处：《运筹学学报》2001年第1期53-62,共10页Operations Research Transactions

基　　金：This work was in part supported by Chinese NSF grat 39830070.

摘　　要：本文对无约束优化问题提出一个自适应信赖域方法，每次迭代都充分利用当前迭代点的信息自动产生一个恰当的信赖域半径，在此区域内，二次模型与原目标函数尽可能一致，避免盲目的尝试，提高了计算效率．文中在通常条件下证明了全局收敛性及局部超线性收敛结果，给出了新算法与传统信赖域方法的数值结果，证实了新方法的有效性．In this paper, a self-adaptive trust region method for unconstrained optimization problems is proposed. By the term self-adaptive', it means that the mathod adaptively generates a suitable trust region radius at each iteration by using information available at the current iteration. Local and global convergence analysis for the new method is given. It is well known that the impact of the trust region radius selection on computational behaviour is quite notable, then the proposed strategy is significant. Neumerical results are given which prove this assertion and show the effectiveness of the proposed method.

关 键 词：无约束优化 信赖域方法 全局收敛性 自适应 迭代 二次模型 目标函数 数值结果 

分 类 号：O224[理学—运筹学与控制论]