关于非线性不等式组Levenberg-Marquardt算法的收敛性(英文)  

ON THE CONVERGENCE OF LEVENBERG-MARQUARDT METHOD FOR NONLINEAR INEQUALITIES

作　　者：何郁波[1] 董晓亮[2] 

机构地区：[1]怀化学院数学系,湖南怀化418008 [2]北方民族大学信息与计算科学学院,宁夏银川750021

出　　处：《数学杂志》2012年第1期25-34,共10页Journal of Mathematics

基　　金：Supported by the Educational Office Foundation of Hunan Province (08C668);the Master,Doctor Foundation of Huaihua University

摘　　要：本文研究了一类非线性不等式组的求解问题.利用一列目标函数两次可微的参数优化问题来逼近非线性不等式组的解,光滑Levenberg-Marquardt方法来求解参数优化问题,在一些较弱的条件下证明了文中算法的全局收敛性,数值实例显示文中算法效果较好.In this article, we study the solutions for a class of nonlinear inequalities. The nonlinear inequalities are approximated by a family of parameterized optimization problems with twice continuously differentiable objective functions, then a smoothing Levenberg-Marquardt method is applied to solve the parameterized optimization problems. The global convergence of the proposed method is established under some weak conditions. Numerical results show that the method performs well.

关 键 词：非线性不等式组 LEVENBERG-MARQUARDT算法 全局收敛 

分 类 号：O224[理学—运筹学与控制论]