一类拟牛顿非单调信赖域算法及其收敛性  

A Quasi-Newton Nonmonotonic Trust Region Algorithm and Its Convergence

作　　者：刘培培[1] 陈兰平[1] 

机构地区：[1]首都师范大学数学科学学院,北京100037

出　　处：《数学进展》2008年第1期92-100,共9页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.60472071);北京市教委科研基金(No.KM200710028001).

摘　　要：本文提出了一类求解无约束最优化问题的非单调信赖域算法.将非单调Wolfe线搜索技术与信赖域算法相结合,使得新算法不仅不需重解子问题,而且在每步迭代都满足拟牛顿方程同时保证目标函数的近似Hasse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.数值结果表明该算法的有效性.In this paper, we propose a new nonmonotonic trust region algorithm for unconstrained optimization. We employ both the nonmonotonic Wolfe line search technique and trust region method. This new algorithm not only does not resolve the subproblem but also satisfies the quasi-Newton condition at each iteration and simultaneously maintains a positive-definite approximation to the Hessian of the objective function. Under mild conditions, the global convergence of the algorithm is proved. Some numerical results show that the new nonmonotonic trust region algorithm is efficiency.

关 键 词：无约束最优化 非单调信赖域方法 拟牛顿方法 非单调线搜索 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]