非线性优化算法理论中一个极限的应用

1引 言 在非线性最优化算法理论中,求解优化问题 min f(x)一般采用迭代形式 x_(k+1)=x_k+λ_kd_k,k=0,1,…,其中λ_k为搜索步长,d_k为搜索方向,λ_k、d_k的适当选取能使算法具有全局收效性: lim inf‖g_k‖=0,其中g_k=f(x_k),{x_k}由算法产生。 步长λ_k的选取实质上是一个对一元函数f(x_k+λd_k)进行线搜索的过程。很多线搜索能保证函数充分递减,即 f(x_k)-f(x_k+λ_kd_k)≥σ(|g_k~Td_k|)/(‖d_k‖) , (1)     

基于梯度的自适应快速布谷鸟搜索算法

针对标准布谷鸟搜索(CS)算法存在全局搜索和局部搜索能力不平衡的缺点, 提出一种基于梯度的自适应快速布谷鸟搜索(GBAQCS)算法. 在改进的算法中, 针对偏好随机游动的步长, 在利用目标函数的梯度决定步长方向的基础上, 首先提出自适应搜索机制平衡了算法的全局搜索和局部搜索能力; 其次提出快速 搜索策略, 充分利用当前鸟巢信息进行精细化搜索, 从而提高算法的搜索精度和收敛速度. 实验结果表明, 相比其他算法, 所提出的改进策略使算法的全局搜索和局部搜索能力保持了相对的平衡, 并提高了算法的收敛性能.     

求解用户平衡与系统最优模型的新算法

近些年,国内外许多学者针对交通规划提出了诸如用户平衡(UE)、系统最优(SO)等模型,但由于交通网络的复杂性,这些模型的求解相对困难,考虑到在一般的UE、S0模型中,其约束条件为线性约束与非负约束,给出一种求解交通规划模型的新算法,算法不需使用任何线搜索,只要通过求解一个简单的二次规划问题得到下降方向即可,最后,将该算法应用到简单的交通网络中,并通过与相继平均法(MSA)进行比较,验证了该算法的收敛速度较快。     

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     

一种新线搜索下的FR共轭梯度法

基于传统的Wolfe线搜索,提出了一种新的非精确线搜索．在无需限制参数σ≤1/2的情况下(即盯的取值范围扩展至0＜σ＜1),证明了FR算法的全局收敛性．数值实验表明了这种线搜索下的FR算法的有效性．     

非单调Frame型直接搜索共轭梯度法

基于非单调的frame概念,提出了一个求解无约束最优化问题的直接搜索共轭梯度算法.该算法不使用充分下降条件而能够在网格(grid)之外进行搜索,这一点不同于GSS(generating setsearch)算法框架,后者为了实现网格之外的搜索必须使用充分下降条件或者移动网格(movinggrids)技术或者有理点阵(r...     

改进的群搜索优化算法

标准的群搜索优化算法(GSO)是一种新的群智能优化算法,适用于解决高维函数的优化问题,而且简单高效,易于实现,但在其优化的后期容易陷入局部最优.为进一步提高其收敛速度和精度,对GSO算法进行了改进.保留其"发现者-加入者"模型,针对GSO算法发现者和游荡者搜索的无目的性,引进最大下降方向和杂交策略,发现者按角度搜索的同时也按最大下降方向进行搜索,游荡者通过基因突变策略的方式生成.通过23个基准测试函数对GSO算法和改进的GSO算法进行测试,结果表明改进的GSO算法在收敛速度和收敛精度上优于标准GSO算法.     

DFP算法的全局收敛性分析

1引言理论分析和大量数值试验表明，在求解（1．1）的各种算法中，拟Newton法是效果最好的一类方法．DFP算法是最早提出的拟Newton法，它首先由Davidon［2］给出并由Fletcher和Powell【3］修改DFP算法的计算步骤如下：算法1．1．1”．取二R”，BIE＊”“”对称正定，k：＝1．2”．计算gb＝7八kh），若gb—0，则终止，得解kk．否则，转入下一步．3O．dk——BK‘gb．4“．进行线搜索确定步长aa．在上面的算法中，步长0。的确定有两种方式：其一，精确线搜索，即。。满足：其M，非精确线搜索．本文考察WOlfe线搜索，即a＆满足：其中o…     

全局较优解引导的人工蜂群算法

人工蜂群算法(ABC)是一种模拟蜜蜂群体寻找优良蜜源的群体智能优化算法.针对人工蜂群算法收敛速度较慢、探索能力较强而开发能力偏弱等问题,提出一种改进的蜂群算法.算法利用更多的较优蜜源位置的信息来引导采蜜蜂和跟随蜂的搜索行为.为了提高算法的全局收敛速度,通过基于混沌策略的方式生成初始化种群,并且在每一代侦察蜂阶段后对全部新蜜源进行反向再搜索.另外,每次蜜蜂邻域搜索之后,采用比较新旧蜜源的花蜜值(而非适应度值)的方法来更新蜜源位置.通过对14个标准测试函数进行仿真实验,结果表明所提出的算法能有效加快收敛速度,提高开发能力和解的精度.     

两分块非凸优化Peaceman-Rachford分裂序列二次规划双步长算法

本文研究大规模两分块非凸约束优化的分解降维算法,提出Peaceman-Rachford (PR)分裂序列二次规划双步长求解方法.本文主要工作和贡献如下:(1)借助PR分裂算法思想将传统二次规划(quadratic programming, QP)子问题的增广Lagrange问题分解为两个小规模QP子问题;(2)通过求解小规模QP产生搜索方向;(3)以增广Lagrange函数为效益函数,沿搜索方向先后进行Armijo线搜索产生双迭代步长,在较弱的条件下保证了算法的全局收敛性、强收敛性和合理的迭代复杂性,克服了Maratos效应;(4)提出乘子新的对称型修正技术;(5)基于一类数学模型和电力系统经济调度模型以及?₂正则二分类问题,对算法进行大量中等规模的比较数值实验,验证了算法的有效性.     

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.     

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].