求解一般非线性互补问题的光滑化方法

在利用Fischer-Burmeister函数将非线性互补问题转化为非线性方程组的基础上,本文通过将信赖域方法与线性搜索方法结合起来,提出了求解一般非线性互补问题的光滑化方法.算法中我们给出了一个特定条件,条件满足时,采用信赖步,条件不满足时.采用梯度步.我们证明了算法具有全局收敛性.在解是R-正则的条件下,收敛速度是Q-超线性/Q-二阶收敛的.     

一簇非线性等式约束优化问题的过滤线搜索修正正割方法

本文提供了一簇新的过滤线搜索修正正割方法求解非线性等式约束优化问题.新算法簇的特点是:用修正正割算法簇中的一个算法获得搜索方向,回代线搜索技术得到步长,过滤准则用来决定是否接受步长,引入二阶校正技术减少不可行性并克服Maratos效应.在合理的假设条件下,分析了算法的总体收敛性.并证明了,通过附加二阶校正步,算法簇克服了Maratos效应,并二步Q-超线性收敛到满足二阶充分最优条件的局部解.数值结果表明了所提供的算法具有有效性.     

采用增广拉格朗日乘子形式的罚函数作线性搜索的递归等式约束二次逼近算法

1.引言 本文所讨论的问题如下: Min f(x) x∈R~n, s.t. c_i(x)=0,i=1,…,q,(1.1) c_i(x)≤0,i=q+1,…,p.解此问题的递归等式约束二次逼近算法,是由Murry(1969)提出,而后由Biggs(1972)发展的.此项研究是从罚函数的轨迹出发,建立一个只包含等式约束的二次规划子问题,从而可用代数的方法求得搜索方向.并沿该方向作线性搜索而完成一次迭代过程.Biggs将二次罚函数作为效应函数用于线性搜索,并证明了该算法具有全局收敛性和局部超线     

一类非线性约束优化的修正正割方法的收敛性

本文修正了一类非线性约束优化的正割方法.通过引入不可微势函数作不精确的一维搜索,证明了修正后的正割算法不仅具有原算法不具备的整体收敛性;而且保持局部两步Q-超线性收敛速率.进一步数值结果表明此算法是非常有效的.     

一类带非精确线性搜索的 DFP 算法

众所周知,以DFP和BFGS为代表的拟牛顿法是解无约束非线性规划问题:min{f(x);x∈R~n}的最常用和最有效的方法之一。但是在实际计算中,若选择步长因子时作的线性搜索“低精度”时,DFP算法的计算效果有时并不理想。而且,尽管1976年Powell证明了带非精确线性搜索的BFGS算法有一步超线性收敛率,1988年吴士泉采用重复使用原始正定矩阵的方法使得算法中用到的变尺度矩阵及其逆阵的迹有界,并且证明这类修改后的DFP算法,对一致凸目标函数,当线性搜索是非精确时,也具有一步超线性收敛率。但是对一般的DFP算法相应的结论是否成立,至今还是一个没有解决的问题。     

Navier-Stokes方程流函数形式两重网格算法的误差分析

对定常Navier-Stokes方程流函数形式两重网格有限元算法进行了误差分析。此方法包括在粗网格上求解一个非线性问题，在细网格上求解一个线性问题，然后再在粗网格上求解一个线性校正问题。分析了包括校正项和不包括校正项两种方法的误差，得出对于任意固定的Beynolds数，能达到最优逼近阶。     

基于核函数求解LCPs的全-Newton步不可行内点算法

本文对P_*(κ)线性互补问题设计了一种基于核函数的全-Newton步不可行内点算法,是对Mansouri等人提出的单调线性互补问题全-Newton步不可行内点算法的改进与推广.算法的主迭代由一个可行步和几个中心步构成且可行步采用小步校正.通过建立和应用一些新的技术性结果,证明了算法的多项式复杂性为O((1+2κ)~(3/2)(1og_2log_264(1+2κ))nlogmax{(x0)Ts0,||r0||}/ε),当k=0时,与当前单调线性互补问题的不可行内点算法最好的迭代复杂性界一致.最后,用Matlab数值实验验证了算法的可行性.     

复杂系统的离散质量生存决策

在复杂系统的质量生存交互决策中,引入了最大质量生存函数W*的概念.为得到W*的数值计算方法,本文系统地研究了离散质量生存(交互)决策和最大离散质量生存函数,推导出最大离散质量生存函数的递归算法,最后用离散算法获得最大Q-生存函数W*的两类离散近似解:有限近似离散近似解和加厚法离散近似解,并给出近似解的收敛性证明.     

等式约束优化一个新的SQP算法

提出了一个处理等式约束优化问题新的SQP算法,该算法通过求解一个增广Lagrange函数的拟Newton方法推导出一个等式约束二次规划子问题,从而获得下降方向．罚因子具有自动调节性,并能避免趋于无穷．为克服Maratos效应采用增广Lagrange函数作为效益函数并结合二阶步校正方法．在适当的条件下,证明算法是全局收敛的,并且具有超线性收敛速度．     

Broyden算法类中两个新的开关算法

<正> 本文从变分的角度,对求解无约束最优化问题 minf(x)x∈R~n给出了Broyden算法中两个新的开关算法。在Wolfe不精确线性搜索的准则下,证明了它们具有全局收敛性,并对超线性收敛进行探讨。计算实例表明,新算法是有效的。     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.