一个求解半正定规划问题的新原始-对偶内点算法

在原始对偶内点算法的设计和分析中,障碍函数对算法的搜索方法和复杂性起着重要的作用.本文由核函数来确定障碍函数,设计了一个求解半正定规划问题的原始-对偶内点算法.这个障碍函数即可以定义算法新的搜索方向,又度量迭代点与中心路径的距离,同时对算法的复杂性分析起着关键的作用.我们计算了算法的迭代界,得出了关于大步校正法和小步校正法的迭代界,它们分别是O(√n log n 10g n/ε)和O(√n log n/ε),这里n是半正定规划问题的维数.最后,我们根据一个算例,说明了算法的有效性以及对核函数的参数的敏感性.     

一个求解半正定规划问题的新原始一对偶内点算法

在原始对偶内点算法的设计和分析中,障碍函数对算法的搜索方法和复杂性起着重要的作用。本文由核函数来确定障碍函数,设计了一个求解半正定规划问题的原始。对偶内点算法。这个障碍函数即可以定义算法新的搜索方向,又度量迭代点与中心路径的距离,同时对算法的复杂性分析起着关键的作用。我们计算了算法的迭代界,得出了关于大步校正法和小步校正法的迭代界,它们分别是O（√n log n log n/c）和O（√n log n/ε）,这里n是半正定规划问题的维数。最后,我们根据一个算例,说明了算法的有效性以及对核函数的参数的敏感性。     

基于指数型核函数的线性规划原始对偶内点算法

给出线性规划原始对偶内点算法的一个单变量指数型核函数.首先研究了这个指数型核函数的性质以及其对应的障碍函数.其次,基于这个指数型核函数,设计了求解线性规划问题的原始对偶内点算法,得到了目前小步算法最好的理论迭代界.最后,通过数值算例比较了基于指数型核函数的原始对偶内点算法和基于对数型核函数的原始对偶内点算法的计算效果.     

二阶锥规划的基于自协调指数核函数的原始-对偶内点算法

基于一个自协调指数核函数, 设计求解二阶锥规划的原始-对偶内点算法. 根据自协调指数核函数的二阶导数与三阶导数的特殊关系, 在求解问题的中心路径时, 用牛顿方向代替了负梯度方向来确定搜索方向. 由于自协调指数核函数不具有``Eligible'性质, 在分析算法的迭代界时, 利用牛顿方法求解目标函数满足自协调性质的无约束优化问题的技术, 估计算法内迭代中自协调指数核函数确定的障碍函数的下降量, 得到原始-对偶内点算法大步校正的迭代界O(2N\frac{\log2N}{\varepsilon}), 这里N是二阶锥的个数. 这个迭代界与线性规划情形下的迭代界一致. 最后, 通过数值算例验证了算法的有效性.     

一个解半正定规划问题的基于广义对数障碍函数的原始对偶内点算法

本文对经典对数障碍函数推广,给出了一个广义对数障碍函数.基于这个广义对数障碍函数设计了解半正定规划问题的原始-对偶内点算法.分析了该算法的复杂性,得到了一个理论迭代界,它与已有的基于经典对数障碍函数的算法的理论迭代界一致.同时,并给出了一个数值算例,阐明了函数的参数对算法运行时间的影响.     

P_*(κ)线性互补问题基于新核函数的大步校正算法（英文）

本文研究了P*(κ)线性互补问题的大步校正原始-对偶内点算法.基于一个强凸且不同于通常的对数函数和自正则函数的新核函数,对具有严格可行初始点的该问题,算法获得的迭代复杂性√为O(1+2κ)n(log n)2lognε,该结果缩小了大步校正内点算法的实际计算与理论复杂性界之间的差距.     

求解正定二次规划的一个全局收敛的滤子内点算法

现有的大多数分类问题都能转化成一个正定二次规划问题的求解.通过引入滤子方法,并结合求解非线性规划的原始对偶内点法,给出求解正定二次规划的滤子内点算法.该算法避免了使用效益函数时选取罚因子的困难,在较弱的假设条件下,算法具有全局收敛性.     

求解最大割问题的半定规划松驰的序列线性规划方法

本文基于最大割问题的半定规划松弛,利用矩阵分解的方法给出了与半定规划松弛等价的非线性规划模型,提出一种序列线性规划方法求解该模型.并在适当的条件下,证明了算法的全局收敛性.数值实验表明:序列线性规划方法在时间上要优于半定规划的内点算法.所以序列线性规划方法能更有效地求解大规模的最大割问题的半定规划松弛.     

基于局部self-concordant障碍函数的全牛顿步多项式时间算法

由Nesterov和Nemirovski[4]创立的self-concordant障碍函数理论为解线性和凸优化问题提供了多项式时间内点算法.根据self-concordant障碍函数的参数,就可以分析内点算法的复杂性.在这篇文章中,我们介绍了基于核函数的局部self-concordant障碍函数,它在线性优化问题的中心路径及其邻域内满足self-concordant性质.通过求解此障碍函数的局部参数值,我们得到了求解线性规划问题的基于此局部Self-concordant障碍函数的纯牛顿步内点算法的理论迭代界.此迭代界与目前已知的最好的理论迭代界是一致的.     

求线性比试和问题的确定性全局优化算法

为求线性比试和问题的全局最优解,本文给出了一个分支定界算法.通过一个等价问题和一个新的线性化松弛技巧,初始的非凸规划问题归结为一系列线性规划问题的求解.借助于这一系列线性规划问题的解,算法可收敛于初始非凸规划问题的最优解.算法的计算量主要是一些线性规划问题的求解.数值算例表明算法是切实可行的.     

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     

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.     

(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 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.     

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.     

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.     

Journal of the Operations Research Society of China Special issue on Operations Research in Healthcare Management

正Guest Editors:Hong Chen,Shanghai Jiao Tong University,Shanghai,China Guohua Wan,Shanghai Jiao Tong University,Shanghai,China David Yao,Columbia University,New York,USA Scope:Healthcare delivery worldwide has been fraught with high cost,low efficiency and poor quality of patient care service.For the field of operations research(OR),healthcare offers some of the biggest challenges as well as best opportunities in     

ANALYSIS IN THEORY AND APPLICATIONS Vol. 30, 2014 CONTENTS

正~~