Convergence and optimality of the adaptive Morley element method

This paper is devoted to the convergence and optimality analysis of the adaptive Morley element method for the fourth order elliptic problem. A new technique is developed to establish a quasi-orthogonality which is crucial for the convergence analysis of the adaptive nonconforming method. By introducing a new parameter-dependent error estimator and further establishing a discrete reliability property, sharp convergence and optimality estimates are then fully proved for the fourth order elliptic problem.     

Wolfe搜索下记忆梯度法的收敛性

本文研究无约束优化问题的记忆梯度算法,分析了Wolfe搜索下该算法的全局收敛性和线性收敛速度。初步数值试验结果表明了算法的有效性。     

一种求解无约束极值问题的无记忆拟牛顿算法

§1.引言 求无约束极值常用的方法,有CG算法、变尺度算法以及拟牛顿算法等等.变尺度算法虽然收敛速度快,但是存贮量大(为O(n~2))。CG算法所需存贮量(为O(n))虽小,但在收敛速度上一般不如变尺度法.因此,本文探索收敛速度快且所需存贮量小的算法,以     

On the semilocal convergence behavior for Halley’s method

The present paper is concerned with the semilocal convergence problems of Halley’s method for solving nonlinear operator equation in Banach space. Under some so-called majorant conditions, a new semilocal convergence analysis for Halley’s method is presented. This analysis enables us to drop out the assumption of existence of a second root for the majorizing function, but still guarantee Q-cubic convergence rate. Moreover, a new error estimate based on a directional derivative of the twice derivative of the majorizing function is also obtained. This analysis also allows us to obtain two important special cases about the convergence results based on the premises of Kantorovich and Smale types.     

A new look at CMRH and its relation to GMRES

CMRH is a Krylov subspace method which uses the Hessenberg process to produce a basis of a Krylov method, and minimizes a quasiresidual. This method produces convergence curves which are very close to those of GMRES, but using fewer operations and storage. In this paper we present new analysis which explains why CMRH has this good convergence behavior. Numerical examples illustrate the new bounds.     

Extension of Henrici's method to matrix sequences

In this paper we generalize the definition of linear convergence to matrix sequences. This new definition is used to establish some new results useful to study the new extension of Henrici's method. A convergence theorem, an algorithm for implementation of this method and some numerical examples are given.     

从常步长梯度方法的视角看不可微凸优化增广Lagrange方法的收敛性

增广Lagrange方法是求解非线性规划的一种有效方法.从一新的角度证明不等式约束非线性非光滑凸优化问题的增广Lagrange方法的收敛性.用常步长梯度法的收敛性定理证明基于增广Lagrange函数的对偶问题的常步长梯度方法的收敛性,由此得到增广Lagrange方法乘子迭代的全局收敛性.     

解等式约束优化的既约Hessian依赖域方法

本文提出了解等式约束优化的一个信赖域方法,该方法以既约Hessian逐步二次规划为基础,它享有信赖域方法与既约Hessian方法的优点,在通常条件下,证明了算法的全局收敛性。     

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.     

GLOBAL CONVERGENCE AND IMPLEMENTATION OF NGTN METHOD FOR SOWING LARGE-SCALE SMRSE NONLINEAR PROGRAMMING PROBLEMS

1. IntroductionConsider the following NLP problemwhere the function f: Re --+ RI and gi: Re - R', j E J are twice continuously dtherentiable.In particular, we discuss the cajse, where the nUmber of variables and the nUmber of constraintsin (1.1) are large and second derivatives in (1.1) are sparse.There are some methods whiCh can solve largesscale problems, e.g. Lancelot in [2] andTDSQPLM in [9]. But they can not take adVantage of sparse structtire of the problem. A newefficient meth…     

数学期望型水平值逼近全局最小值的方法

郑权在1978年提出的一种积分水平集算法概念性算法.由于水平集一般情况下难以求出,此算法通过Monte-Carlo随机取点来实现.本文提出了数学期望型水平值逼近全局最小值的概念性算法,它利用了相对熵主要思想,通过改变重要样本密度函数,克服了郑权算法水平集不易求得而难以求出水平值的困难.本文还给出了求全局最小值的收敛准则并证明了它的渐进收敛性.     

弦割法与Muller法收敛阶的新证明方法

弦割法、Muller法与牛顿法一样,都是求解非线性方程的著名算法之一.然而在目前众多优秀的数值分析教材或论著中.关于弦割法和Muller法收敛阶的证明过程都是比较复杂的,无一例外的都是借助于差分方程的求解.本文对这两个算法的收敛阶给出了一种新的简单、直接的证明方法,达到了与牛顿法收敛阶证明方法的统一,同时还能够方便地求...     

Convergence of descent method with new line search

An efficient descent method for unconstrained optimization problems is line search method in which the step size is required to choose at each iteration after a descent direction is determined. There are many ways to choose the step sizes, such as the exact line search, Armijo line search, Goldstein line search, and Wolfe line search, etc. In this paper we propose a new inexact line search for a general descent method and establish some global convergence properties. This new line search has many advantages comparing with other similar inexact line searches. Moreover, we analyze the global convergence and local convergence rate of some special descent methods with the new line search. Preliminary numerical results show that the new line search is available and efficient in practical computation.     

Wolfe搜索下的一种共轭梯度法

研究无约束优化问题的共轭梯度算法,提出了一种计算主要参数的新形式,分析了Wolfe搜索下该算法的全局收敛性.     

无约束优化问题的一个下降方法

本文研究了无约束优化问题.利用当前和前面迭代点的信息以及曲线搜索技巧产生新的迭代点,得到了一个新的求解无约束优化问题的下降方法.在较弱条件下证明了算法具有全局收敛性.当目标函数为一致凸函数时,证明了算法具有线性收敛速率.初步的数值试验表明算法是有效的.     

A sharp convergence estimate for the method of subspace corrections for singular systems of equations

This paper is devoted to the convergence rate estimate for the method of successive subspace corrections applied to symmetric and positive semidefinite (singular) problems. In a general Hilbert space setting, a convergence rate identity is obtained for the method of subspace corrections in terms of the subspace solvers. As an illustration, the new abstract theory is used to show uniform convergence of a multigrid method applied to the solution of the Laplace equation with pure Neumann boundary conditions.

     

求解单调AVI问题的一个新方法

本文提出了一个求解单调AVI问题的新方法，并在无任何附加条件下，证明了它的收敛性和线性收敛率。     

Fixed point iterations coupled with relaxation factors and inertial effects

This paper deals with a general fixed point method which unifies relaxation factors and a two step inertial type extrapolation. These strategies are intended to improve the convergence of many existing algorithms. A convergence theorem, which improves the known ones, is established in this new setting.     

用于求根问题的一个基于Thiele连分式的四阶收敛的迭代方法

利用截断的Thiele连分式,本文给出了一个求解非线性单变量方程的单步迭代方法,并证明了所提出的迭代方法具有四阶收敛性.最后,本文通过一些数值例子说明了所提出的方法的有效性和表现.     

一类新的曲线搜索下的多步下降算法

提出一类新的曲线搜索下的多步下降算法,在较弱条件下证明了算法具有全局收敛性和线性收敛速率.算法利用前面多步迭代点的信息和曲线搜索技巧产生新的迭代点,收敛稳定,不用计算和存储矩阵,适于求解大规模优化问题.数值试验表明算法是有效的.