关于不等式约束的信赖域算法

对于具有不等式约束的非线性优化问题，本文给出一个依赖域算法，由于算法中依赖区域约束采用向量的∞范数约束的形式，从而使子问题变二次规划，同时使算法变得更实用。在通常假设条件下，证明了算法的整体收敛性和超线性收敛性。     

凸约束优化的非单调信赖域算法的收敛性

本文对凸约束优化问题提出一类新的非单调信赖域算法，在二次模型Hesse矩阵{Bk}一致有界条件下，证明了算法具有强收敛性；在{Bk}线性增长的条件下，证明了算法具有弱收敛性；这推广了现有约束或凸约束优化问题的各种信赖域算法，改进了收敛性结果。     

非线性约束条件下一个超线性收敛的可行方法

在本文中，我们对非线性不等式约束条件下的非线性优化问题给出了一个新的ＳＱＰ类可行方法．此算法不但结构简单、易于计算，并且在适当的假设条件下，我们证明了算法具有全局收敛性及超线性收敛性     

无严格互补松驰条件的序列线性方程组新算法

该文通过构造特殊形式的有效集来逼近KKT点处的有效集，给出了一个任意初始点下的序列线性方程组新算法，并证明了该算法在没有严格互补松驰条件的情况下具有全局收敛性和一步超线性收敛性。      

混合互补问题的光滑逼近法

提出了求解混合互补问题的一个光滑逼近算法，并在一定条件下证明了该算法的全局收敛性．     

变分不等式问题的全局收敛性算法

本文给出了带一般凸约束的变分不等式问题的算法，并在多种线性搜索下证明了算法的全局收敛性。     

限制PR共轭梯度法及其全局收敛性

PR共轭梯度法是求解大型无约束优化问题的有效算法之一，但是算法的全局收敛性在理论上一直没有得到解决。本文将PR共轭梯度法中的参数β加以限制，提出了限制R共轭梯度法，证明了Armijo搜索下算法的全局收敛性、数值试验表明算法是很有效的。     

m步非线性多重分裂Newton法的收敛性

本文讨论了多重分裂算法在求解一类非线性方程组的全局收敛性和单侧收敛性．当用研步Newton法来代替求得每个非线性多重分裂子问题的近似解时，同样给出相应收敛性结论．数值算例证实了算法的有效性．     

广义异步矩阵多分裂向前向后松驰算法

本文建立了一类广义异步矩阵多分裂向前向后松驰算法，并在系数矩阵是Ｈ－矩阵的条件下，证明了这类算法的收敛性。     

在退化情况下的一个可行方向法

本文给出了一个新的非线性约束优化的可行方向法．该算法适用于退化问题(积极约束梯度线性相关)，算法结构简单，在适当条件下，证明此算法具有全局收敛性．数值实验表明算法是有效的．     

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.     

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].