一个锥模型的自适应信赖域算法及其收敛性  

A SELF-ADAPIVE TRUST REGION METHOD AND ITS CONVERGENCE WITH THE CONIC MODEL

作　　者：冯琳[1] 段复建[2] 

机构地区：[1]重庆文理学院数学与财经学院,重庆402160 [2]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《数学杂志》2016年第1期144-156,共13页Journal of Mathematics

基　　金：国家自然科学基金(11061011);广西自然科学基金(2011GXNSFA018138);重庆文理学院课题(Y2013sc42)

摘　　要：本文研究了无约束最优化问题的基于锥模型的自适应信赖域算法.利用理论分析得到一个新的自适应信赖域半径.算法在每步迭代中以变化的速率、当前迭代点的信息以及水平向量信息调节信赖域半径的大小.从理论上证明了新算法的全局收敛性和Q-二阶收敛性.用数值试验验证了新算法的有效性.推广了已有的自适应信赖域算法的可行性和有效性.In this paper,we study a self-adaptive trust region algorithm based on the conic model for unconstrained optimization problems.A new self-adaptive trust region radius is produced under theoretical analysis.At each iterative,the trust region radius is updated at a variable rate,the information at the current point and the level vector information.We analyze the global convergence and Q-quadratic convergence of the new method.Numerical results are also presented to test the efficiency of the new method which extend the application and efficiency of self-adaptive trust region algorithms.

关 键 词：无约束最优化 信赖域方法 锥模型 自适应 收敛性 

分 类 号：O224.2[理学—运筹学与控制论]