关于广义Newton法的收敛性问题  

ON THE CONVERGENCE OF GENERALIZED NEWTON METHOD

作　　者：张建军[1] 王德人[1] 

机构地区：[1]上海大学数学系,上海201800

出　　处：《应用数学学报》1999年第4期513-521,共9页Acta Mathematicae Applicatae Sinica

摘　　要：本文在较弱的条件下，证明了B-可微方程组的广义Newton法的局部超线性收致性，为该算法直接应用于非线性规划问题、变分不等问题以及非线性互补问题等提供了理论依据．最后，本文绘出了广义Newton法付之实践的具体策略．数值结果责明，算法是行之有效的．This paper inverstigates generalized Newton method for solving B-differentiable equations.We prove local superlinear convergence results under some weaker conditions.Therefore, we establish theoretical foundation for the method to be directly applied to nonlinear programs, vaxiational inequality and complemelltarity problems. Finally, we discuss bolemelitations for generalized Newton method applied to practical problems. Numerical results show that the algorithIn is effective.

关 键 词：B-可微方程组 广义牛顿法 收敛性 非线性规划 

分 类 号：O242.23[理学—计算数学] O221.2[理学—数学]