带线搜索的修正拟牛顿非单调信赖域算法  

A Modified Quasi-Newton Trust-Region Algorithm with Nonmonotonic Wolfe Line Search

作　　者：杨洁[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）》2010年第1期1-5,共5页Journal of Capital Normal University：Natural Science Edition

基　　金：北京市教委科研基金(KM200710028001)资助

摘　　要：提出了一类新的求解无约束最优化问题的非单调信赖域算法.不同于传统的非单调信赖域算法,此算法在每步都采用非单调W olfe线搜索得到下一个迭代点.这样得到的新算法不仅不需重解子问题,而且在每步迭代满足新拟牛顿方程同时保证目标函数的近似Hessen阵Bk的正定性.在较弱的条件下,证明了此算法的全局收敛性.数值结果表明该算法的有效性.In this paper, we present a modified quasi-Newton nonmonotonic trust region algorithm with Wolfe line search. Unlike traditional nonmonotonic trust region algorithms, our algorithm gets the next point by the nonmonotonic Wolfe line search at each iteration. This new algorithm not only does not resolve the subproblem but also satisfies the modified 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 numerical results show its efficiency.

关 键 词：无约束最优化 信赖域算法 非单调线搜索 修正拟牛顿校正 全局收敛性. 

分 类 号：O224[理学—运筹学与控制论]