多场址问题的信赖域算法

多场址问题是一类重要的不可微凸规划问题，国内外已有许多学者对其进行研究，并提出了一 算法。但如文「２」中所述，大多数算法或无收敛收保证，或在较强的条件下才保证收敛，本文提出一类解多场址问题的信赖域算法，并在极弱的条件下证明该类算法的全局收敛性。     

在闭凸集上连续型多场址的最优选择

本文考虑带有约束的连续型多场址问题(CEMFLC).对于连续型多场址问题(CEMFLC),我们给出了在闭集上选择最优场址的算法,证明了该算法是全局收敛的,最后,我们指出这一算法可用于解有约束或无约束的的高离散型多场址问题(EMFL),而且简化了(EMFL)问题现有的一些算法.     

最优场址问题的研究进展

３０年代以来，最优场址问题一直是运筹学界阳活跃的研究领域之一。此问题具有深镔实验背景和广泛的实用价值。本文综述了最优场址问题研究进展并对其发展历史进行了简单的回顾，主要介绍近年来最优场址问题研究的一些重要成果，对每一种成果进行了基本的评论。     

在闭凸集上求min sum from i=1 to n c_i||x-a_i||型最优场址

对于min sum from i=1 to n c_i||x-α_i||型最优场址,早在1937年E.Weiszfeld就给出了一种简单的迭代算法,但他对于收敛性的证明是很不严格的。后来波兰应用数学工作者在选择邮局的最优局址时也曾采用过此法,而关于收敛性仍未解决。近年来,H.W.Kuhn于     

Fermat场址问题的信赖域算法

1 问题及预备引理 设R~n是n维欧氏空间，a_i∈R~n,i=1,2,…，t是t个不共线的点，w_i>0,i=1,2,…,t,┃·┃表欧氏范数，著名的Fermat场址问题是     

线性约束下的共轭投影梯度法及其超线性收敛性

本文考虑线性约束非线性规划问题，提出了一类共轭投影梯度法，证明了算法的全局收敛性，并对算法的二次终止性，超线性收敛特征进行了分析，算法的优点是（１）采用计算机上实现的Ａｒｍｉｊｏ线性搜索规则，（２）初始点不要求一定是可行点，可以不满足线性等式约束，（３）具有较快的收敛速度。     

小议算法中的斐波那契数列

对于苏教版必修3<算法初步>一章节中,其知识内容要求不高,且高考对"算法与流程图"的考点要求为A级要求.对于本章只要求同学们能看懂流程图,并能了解算法的一些基本步骤和含义.虽然高考对本章要求不高,但并不表示它没有很深的研究价值.     

一类MPEC问题的SQP算法

本文研究带线性互补约束规划问题的 SQP算法 .该算法不要求精确计算初值 ,是针对初值非精确计算情形的新算法 ,证明了该算法的收敛性 .     

非线性半定规划的逐次线性化柔性惩罚法

针对非线性不等式约束半定规划问题提出一种新的逐次线性化方法, 新算法既不要求罚函数单调下降, 也不使用过滤技巧, 尝试步的接受准则仅仅依赖于目标函数和约束违反度, 罚函数中对应于成功迭代点的罚因子不需要单调增加. 新算法或者要求违反约束度量有足够改善, 或者在约束违反度的一个合理范围内要求目标函数值充分下降, 在通常假设条件下, 分析了新算法的适定性及全局收敛性. 最后, 给出了非线性半定规划问题的数值试验结果, 结果表明了新算法的有效性.     

非线性半定规划的逐次线性化柔性惩罚法（英文）

针对非线性不等式约束半定规划问题提出一种新的逐次线性化方法,新算法既不要求罚函数单调下降,也不使用过滤技巧,尝试步的接受准则仅仅依赖于目标函数和约束违反度,罚函数中对应于成功迭代点的罚因子不需要单调增加.新算法或者要求违反约束度量有足够改善,或者在约束违反度的一个合理范围内要求目标函数值充分下降,在通常假设条件下,分析了新算法的适定性及全局收敛性.最后,给出了非线性半定规划问题的数值试验结果,结果表明了新算法的有效性.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

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.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

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].