含参变量的三阶方向牛顿法及其收敛性

通过递推关系归纳迭代公式的讨论,研究含多个未知数的非光滑方程组及其收敛性,并以此证明希尔伯特空间上的含参变量的实系数非线性方程组的三阶方向牛顿法的半局部收敛性,给出解的存在性以及先验误差界.     

一维凸函数牛顿法的全局收敛性及其应用

牛顿法是求解非线性方程F（x)＝0的一种经典方法。在一般假设条件下，牛顿法只具有局部收敛性。本文证明了一维凸函数牛顿法的全局收敛性，并且给出了它在全局优化积分水平集方法中的应用。     

非光滑方程的方向牛顿法

通过引入广义梯度,将求解含n个未知量方程的方向牛顿法推广到非光滑的情形.证明了该方法在半光滑条件下的收敛性定理,给出了解的存在性以及先验误差界.     

牛顿法的改进及其在Banach空间中收敛性

牛顿法是求解非线性方程(组)的一种经典方法,本文在Banach空间中对经典牛顿法加以了改进,研究了其收敛性,改进后的牛顿法具有更广泛的应用前景.     

非光滑方程组牛顿法的全局收敛性分析

通过定义一种新的*-微分,本文给出了局部Lipschitz非光滑方程组的牛顿法,并对其全局收敛性进行了研究.该牛顿法结合了非光滑方程组的局部收敛性和全局收敛性.最后,我们把这种牛顿法应用到非光滑函数的光滑复合方程组问题上,得到了较好的收敛性.     

非线性方程的数值迭代法及其半局部收敛性

本文主要探讨非线性(算子)方程的数值迭代法及其半局部收敛性.在迭代方法部分,讨论了迭代法的构造技巧,主要可分为线性逼近、积分插值、Adomian级数分解、Taylor展开以及多步迭代等;在半局部收敛性部分,讨论了半局部收敛性的收敛条件以及证明收敛性的方法,包括递归法和优界序列法,同时还讨论了优界序列法所使用的优界函数.     

非线性方程的数值迭代法及其半局部收敛性北大核心CSCD

本文主要探讨非线性(算子)方程的数值迭代法及其半局部收敛性.在迭代方法部分,讨论了迭代法的构造技巧,主要可分为线性逼近、积分插值、Adomian级数分解、Taylor展开以及多步迭代等;在半局部收敛性部分,讨论了半局部收敛性的收敛条件以及证明收敛性的方法,包括递归法和优界序列法,同时还讨论了优界序列法所使用的优界函数.     

一类非光滑方程组的牛顿法及全局收敛性

借助于一种新的微分 - -微分 ,本文给出极大值函数及其光滑复合的非光滑方程组的牛顿法 .最后证明了该牛顿法具有全局收敛性 .     

基于非单调线搜索非拟牛顿法的全局收敛性

本文就非拟牛顿法在无约束最优化问题上，对采用非单调线搜索的情况下是否具有全局收敛性进行了研究，在目标函数满足一致凸的条件下，证明了非拟牛顿族是全局收敛的．     

On Convergence Domains of Newton's and Modified Newton Methods

ABSTRACT

We analyze convergence domains of Newton's and the modified Newton methods for solving operator equations in Banach spaces assuming first that the operator in question is ω-smooth in a ball centered at the starting point. It is shown that the gap between convergence domains of these two methods cannot be closed under ω-smoothness. Its exact size for Hölder smooth operators is computed. Then we proceed to investigate their convergence domains under regular smoothness. As our analysis reveals, both domains are the same and wider than their counterparts in the previous case.     

Local Convergence of the Interior-Point Newton Method for General Nonlinear Programming

In this paper, a formulation for an interior-point Newton method of general nonlinear programming problems is presented. The formulation uses the Coleman-Li scaling matrix. The local convergence and the q-quadratic rate of convergence for the method are established under the standard assumptions of the Newton method for general nonlinear programming.     

Composition operators on the Newton space

We investigate properties of composition operators C? on the Newton space (the Hilbert space of analytic functions which have the Newton polynomials as an orthonormal basis). We derive a formula for the entries of the matrix of C? with respect to the basis of Newton polynomials in terms of the value of the symbol ? at the non-negative integers. We also establish conditions on the symbol ? for boundedness, compactness, and self-adjointness of the induced composition operator C?. A key technique in obtaining these results is use of an isomorphism between the Newton space and the Hardy space via the Binomial Theorem.     

关于Brown方法的半局部收敛性

在本文中,我们讨论解非线性方程组的Brown方法的半局部收敛性。通过对Brown方法的算法结构作深入的分析,我们将Brown方法变换成带有特殊误差项的近似Newton法,基于这种等价变形,我们建立了Brown方法的半局部收敛定理,从而完善了Brown方法的收敛理论。     

Convergence of Directional Methods under mild differentiability and applications

A semilocal convergence analysis for Directional Methods under mild differentiability conditions is provided in this study. Using our idea of recurrent functions, we provide sufficient convergence conditions as well as the corresponding errors bounds. The results are extended to hold in a Hilbert space setting and a favorable comparison is provided with earlier works [6], [7], [8], [9], [10], [11] and [20]. Numerical examples are also provided in this study.     

Convergence of a generalized Newton and an inexact generalized Newton algorithms for solving nonlinear equations with nondifferentiable terms

In this paper, we consider two versions of the Newton-type method for solving a nonlinear equations with nondifferentiable terms, which uses as iteration matrices, any matrix from B-differential of semismooth terms. Local and global convergence theorems for the generalized Newton and inexact generalized Newton method are proved. Linear convergence of the algorithms is obtained under very mild assumptions. The superlinear convergence holds under some conditions imposed on both terms of equation. Some numerical results indicate that both algorithms works quite well in practice.      

堆浸工艺中浸润面的牛顿迭代计算方法

为了研究堆浸工艺的机理,用牛顿迭代公式寻求浸润面的非线性方程的数值解,经过14次迭代的误差达到了10^-6,说明此算法收敛有效。