两两NQD列的收敛性质

本文首先给出两两 ＮＱＤ列的 Ｋｏｌｍｏｇｏｒｏｖ型不等式，进而讨论两两 ＮＱＤ列的收敛性质，获得了与独立情形一样的Ｂａｕｍ和Ｋａｔｚ完全收敛定理，几乎达到独立惰形著名的Ｍａｒｃｉｎｋｉｅｗｉｃｚ强大数定律、三级数定理等结果．  

A nonsmooth version of Newton's method

Newton's method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized Jacobian instead of the derivative. This extension includes the B-derivative version of Newton's method as a special case. Convergence theorems are proved under the condition of semismoothness. It is shown that the gradient function of the augmented Lagrangian forC ²-nonlinear programming is semismooth. Thus, the extended Newton's method can be used in the augmented Lagrangian method for solving nonlinear programs.This author's work is supported in part by the Australian Research Council.This author's work is supported in part by the National Science Foundation under grant DDM-8721709.  

Iterative Algorithms for Nonlinear Operators

Iterative algorithms for nonexpansive mappings and maximal monotoneoperators are investigated. Strong convergence theorems areproved for nonexpansive mappings, including an improvement ofa result of Lions. A modification of Rockafellar’s proximalpoint algorithm is obtained and proved to be always stronglyconvergent. The ideas of these algorithms are applied to solvea quadratic minimization problem.  

层次分析法权重计算方法分析及其应用研究

介绍层次分析法的基本概念,同时也分析了层次分析法权重的计算方法及应用,层次分析法的计算方法有四种方法:几何平均法、算术平均法、特征向量法、最小二乘法,以往的文献利用层次分析法解决实际问题时,都是采用其中的某一种方法求权重向量,不同的方法会导致结果有些偏差,将对一具体实例,采用四种计算方法分别得出权重向量再进行排序和综合分析,这样可以避免采用单一方法所产生的偏差,得出的结论将更全面、更有效。  

An Iterative Approach to Quadratic Optimization

Assume that C ₁, . . . , C _N are N closed convex subsets of a real Hilbert space H having a nonempty intersection C. Assume also that each C _i is the fixed point set of a nonexpansive mapping T _i of H. We devise an iterative algorithm which generates a sequence (x _n ) from an arbitrary initial x ₀H. The sequence (x_n) is shown to converge in norm to the unique solution of the quadratic minimization problem min _xC (1/2)Ax, x–x, u, where A is a bounded linear strongly positive operator on H and u is a given point in H. Quadratic–quadratic minimization problems are also discussed.  

半平面上有限级Dirichlet级数的正规增长

本文在一般的指数条件下,研究了右半平面上有限级Ｄｉｒｉｃｈｌｅｔ级数的增长性和正规增长性与它的系数的关系,得到了两个充要条件．  

无限级Dirichlet级数

本文研究了右半平面上无限级的Ｄｉｒｉｃｈｌｅｔ级数及随机Ｄｉｒｉｃｈｌｅｔ级数．这里我们给出一个较宽的系数条件，并证明在一定意义上是最好的；计算无限级Ｄｉｒｉｃｈｌｅｔ级数的精确级；把随机级数的研究引向一般得多的非同分布情况，并得到右半平面上非同分布的无限级随机Ｄｉｒｉｃｈｌｅｔ级数几乎必然（ａ．ｓ．）以虚轴上的每一点为没有有限例外值的Ｂｏｒｅｌ点的结论．  

Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities

The smoothing Newton method for solving a system of nonsmooth equations , which may arise from the nonlinear complementarity problem, the variational inequality problem or other problems, can be regarded as a variant of the smoothing method. At the th step, the nonsmooth function is approximated by a smooth function , and the derivative of at is used as the Newton iterative matrix. The merits of smoothing methods and smoothing Newton methods are global convergence and convenience in handling. In this paper, we show that the smoothing Newton method is also superlinearly convergent if is semismooth at the solution and satisfies a Jacobian consistency property. We show that most common smooth functions, such as the Gabriel-Moré function, have this property. As an application, we show that for box constrained variational inequalities if the involved function is -uniform, the iteration sequence generated by the smoothing Newton method will converge to the unique solution of the problem globally and superlinearly (quadratically).

  

A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities

In this paper we take a new look at smoothing Newton methods for solving the nonlinear complementarity problem (NCP) and the box constrained variational inequalities (BVI). Instead of using an infinite sequence of smoothing approximation functions, we use a single smoothing approximation function and Robinson’s normal equation to reformulate NCP and BVI as an equivalent nonsmooth equation H(u,x)=0, where H:ℜ ²ⁿ →ℜ ²ⁿ , u∈ℜ ⁿ is a parameter variable and x∈ℜ ⁿ is the original variable. The central idea of our smoothing Newton methods is that we construct a sequence {z ^k =(u ^k ,x ^k )} such that the mapping H(·) is continuously differentiable at each z ^k and may be non-differentiable at the limiting point of {z ^k }. We prove that three most often used Gabriel-Moré smoothing functions can generate strongly semismooth functions, which play a fundamental role in establishing superlinear and quadratic convergence of our new smoothing Newton methods. We do not require any function value of F or its derivative value outside the feasible region while at each step we only solve a linear system of equations and if we choose a certain smoothing function only a reduced form needs to be solved. Preliminary numerical results show that the proposed methods for particularly chosen smoothing functions are very promising. Received June 23, 1997 / Revised version received July 29, 1999?Published online December 15, 1999  

拟二次系统的广义焦点量与极限环分枝

本文给出了拟二次系统的前18个奇点量和可积性条件,由此统一解决了几类实平面微分自治系统的初奇点、高次奇点以及无穷远点的中心焦点判定与极限环分枝问题.