非线性不等式系统带折线步的信赖域方法及其收敛性  

On the Convergence of Trust Region Method With Dogleg Step for Nonlinear Inequalities Systems

作　　者：何郁波[1] 林晓艳[1] 

机构地区：[1]怀化学院数学与应用数学系,湖南怀化418008

出　　处：《应用数学和力学》2013年第11期1216-1224,共9页Applied Mathematics and Mechanics

基　　金：湖南省教育厅资助重点项目(08A503);湖南省普通高校青年骨干教师培养基金资助项目(湘教通[2012]510号)

摘　　要：针对一类非线性不等式系统求解的问题,利用一系列目标函数二次可微的带参数优化问题来逐次逼近非线性不等式系统的解,从而提出了针对参数最优化问题带折线步的信赖域算法.在较弱的条件下,算法的全局收敛性得到了保证.数值试验显示算法有效.The solutions of a class of nonlinear inequalities were studied.The nonlinear inequalities were approximated by a family of parameterized optimization problems with twice continuously differentiable objective functions, then a smoothing trust region method with dogleg steps was applied to solve the parameterized optimization problems. The global convergence of the proposed method was established under some weak conditions. Numerical results show that the method performs well.

关 键 词：非线性不等式系统 信赖域算法 Cauchy点 折线步 全局收敛 

分 类 号：O178.2[理学—数学]