伪牛顿信赖域算法及其收敛性  

A Pseudo-Newton trust region Algorithm and its Convergence

作　　者：陈兰平[1] 任洪涛[1] 焦宝聪[1] 

机构地区：[1]首都师范大学数学科学学院,北京100048

出　　处：《首都师范大学学报（自然科学版）》2011年第1期1-8,共8页Journal of Capital Normal University：Natural Science Edition

摘　　要：本文提出了一类新的求解无约束最优化问题的信赖域算法.新算法将Goldstein线搜索技术与信赖域方法相结合,并通过伪Newdon-δ族校正公式计算信赖域子问题中的Bk,使算法不仅不需重解子问题,而且每步迭代都满足弱拟牛顿方程,保证了目标函数的近似Hesse阵Bk的正定性.在适当的条件下,证明了此算法的全局收敛性和Q-二次收敛性.数值试验结果表明了该算法的有效性.In this paper,a new trust region algorithm for unconstrained optimization is presented.Unlike traditional trust region algorithms,our algorithm gets the next point by the Goldstein line search at each iteration.This new algorithm not only does not resolve the subproblem but also satisfies the non-quasi-Newton condition at each iteration and simultaneously maintains a positive-definite approximation to the Hessian of the objective function.Under mild conditions,we prove the global convergence and Q-quadratic convergence of the algorithm.Numerical results show its efficiency.

关 键 词：无约束最优化 信赖域方法 伪Newdon-δ方法 GOLDSTEIN线搜索 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]