求解非光滑凸规划的一种混合束方法

提出一种求解非光滑凸规划问题的混合束方法. 该方法通过对目标函数增加迫近项, 且对可行域增加信赖域约束进行迭代, 做为迫近束方法与信赖域束方法的有机结合, 混合束方法自动在二者之间切换, 收敛性分析表明该方法具有全局收敛性. 最后的数值算例验证了算法的有效性．     

基于改进的粒子群算法求解供应链网络均衡问题

传统的供应链求解方法为投影法,针对其要对投影进行计算,十分复杂的缺点,提出用改进的粒子群算法求解供应链均衡问题,利用动态异步调整学习因子来有效的提高了算法搜索能力与精度。本文介绍了供应链网络均衡问题转变为无约束优化问题的方法,然后用改进的粒子群优化算法进行求解。通过四个数值算例,将实验结果与标准粒子群算法、蜂群算法、学习因子同步变化的粒子群算法进行比较,验证了改进的粒子群优化算法在解决供应链网络均衡问题中的有效性与优越性,为供应链网络求解提供了一种新的方法。     

惩罚框架下求解广义Nash均衡问题的分解算法

广义Nash均衡问题(GNEP),是非合作博弈论中一类重要的问题,它在经济学、管理科学和交通规划等领域有着广泛的应用.本文主要提出一种新的惩罚算法来求解一般的广义Nash均衡问题,并根据罚函数的特殊结构,采用交替方向法求解子问题.在一定的条件下,本文证明新算法的全局收敛性.多个数值例子的试验结果表明算法是可行的,并且是有效的.     

求解带有三元函数的广义半均衡问题的预测校正法

本文介绍一类新的均衡问题--带有三元函数的广义半均衡问题.借助于辅助原理法提出了求解此类问题的一个三步预测-校正迭代法,并分析了算法的收敛性.     

非线性互补约束均衡问题的一个滤子SQP算法

提出了—个求解非线性互补约束均衡问题的滤子SQP算法.借助Fischer-Burmeister函数把均衡约束转化为—个非光滑方程组,然后利用逐步逼近和分裂思想,给出—个与原问题近似的一般的约束优化.引入滤子思想,避免了罚函数法在选择罚因子上的困难.在适当的条件下证明了算法的全局收敛性,部分的数值结果表明算法是有效的.     

竞争市场均衡问题的内点算法

本文应用最优化方法求解经济学中的经典问题-竞争市场均衡问题.本文对Ye的算法(Ye首先提出了解Fisher问题的原始-对偶路径跟踪算法)做了改进,分别给出了步长调整和迭代方向分解后的原始-对偶路径跟踪算法,并对算法做了理论证明和复杂性分析.最后分析了初始点的求法,做了初步的数值计算.计算结果表明算法能在有效时间内求得问题的解.     

混合型装配线平衡问题求解方法研究

对混合型装配线平衡问题进行了描述和数学建模,提出一种启发式求解算法,求解目标是最小化工作站数目.为进一步优化求解结果,对启发式算法求解的结果进行仿真研究,分析各工作站的工作率、等待率和阻塞率,并以此为依据调整部分作业任务的分配,允许不同品种产品的相同作业任务安排在不同的工作站中,以对求解结果进行修正,进一步均衡各工作站的作业量.该求解方法既简化了求解过程,又兼顾到了系统的瞬时特性和作业任务的不可拆分性对求解结果的影响,实例分析验证了方法的有效性.     

线性互补问题均衡解的存在形式与识别方法

研究了线性互补问题均衡解的存在形式与判定方法,给出了线性互补问题有解的充要条件,得到了带有几类特殊系数矩阵的线性互补问题的解的性质.在此基础上设计了求解线性互补问题均衡解的直接算法.     

一类多个下层的双层规划问题

本文研究了一类多个下层的双层规划问题.利用文[1]有关理论与方法,获得了该类多下层双层规划问题与一类广义纳什均衡问题的联系,然后通过寻找该广义纳什均衡问题的均衡点求解该双层规划问题.同时给出了一种求解此类广义纳什均衡问题的算法,并进行了一定的理论分析与数值计算.     

基于变权综合的多目标规划均衡解

研究多目标规划的求解问题,提出了一种新的基于变权综合求解方法.用变权综合理论提出了惩罚性均衡解,并且证明了它是多目标规划有效解,并且给出求解均衡有效解的步骤.通过实际例题表明,该方法是正确有效解决了多目标规划问题,与线性加权法和平方加权和法相比而言,具有较好的综合均衡性能.     

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 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.     

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.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.