An Extended Ant Colony Algorithm and Its Convergence Analysis

In this work, we propose a stochastic algorithm for solving combinatorial optimization problems. The procedure is formulated within the Ant Colony Optimization (ACO) framework, and extends the so-called Graph-based Ant System with time-dependent evaporation factor, (GBAS/tdev) studied in Gutjahr (2002). In particular, we consider an ACO search procedure which also takes into account the objective function value. We provide a rigorous theoretical study on the convergence of the proposed algorithm. Further, for a toy example, we compare by simulation the rate of convergence of the proposed algorithm with those from the Random Search (RS) and from the corresponding procedure in Gutjahr (2002).AMS 2000 Subject Classification: 9OC15, 9OC27     

On the Convergence Acceleration of Composite Sequence Transformation

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Stability of Doob—Meyer Decomposition Under Extended Convergence

In what follows, we consider the relation between Aldous‘s extended convergence and weak convergence of filtrations. We prove that, for a sequence (X^n) of Ft^n )-special semimartingales, with canonical decomposition X^n =M^n A^n, if the extended convergence (X^n,F.^n)→(X,T. ) holds with a quasi-left continuous (Ft)-special semimartingale X = M A, then, under an additional assumption of uniform integrability,we get the convergence in probability under the Skorokhod topology: M^n↑P→M and A^n↑P→ A.     

递推阻尼最小二乘法的收敛性与稳定性

递推最小二乘法是参数辨识中最常用的方法,但容易产生参数爆发现象.因此对一种更稳定的辨识方法——递推阻尼最小二乘法进行了收敛特性的分析.在使用算法之前先归一化测量向量,结果表明,参数化距离收敛于一个零均值随机变量,并且在持续激励条件下,适应增益矩阵的条件数有界.参数化距离的方差有界.     

基于有效约束识别技术的一个SSLE算法及其收敛性分析

基于一个有效约束识别技术, 给出了具有不等式约束的非线性最优化问题的一个可行SSLE算法. 为获得搜索方向算法的每步迭代只需解两个或三个具有相同系数矩阵的线性方程组. 在一定的条件下, 算法全局收敛到问题的一个KKT点. 没有严格互补条件, 在比强二阶充分条件弱的条件下算法具有超线性收敛速度.     

延迟积分微分方程线性多步方法的稳定性分析

考虑带常延迟的延迟积分微分方程线性系统零解的渐近稳定性，本文采用拉格朗日插值的线性多步方法，探讨了系统数值方法的线性稳定性。证明了所有A-稳定且强零-稳定的Pouzet型线性多步方法能够保持原线性系统的延迟不依赖稳定性。     

蝙蝠算法收敛性分析

将蝙蝠算法简化到一维的单个蝙蝠,定义了速度和位置更新的两种模式,利用特征方程的方法分别对其进行了收敛性分析,得出模式2比模式1具有更好的收敛性,同时给出了在模式2下的参数选取方法.最后通过数值仿真实验,验证了相关分析的正确性.     

关于有限族Lipschitz映射多步Ishikawa迭代算法的收敛性及其应用

本文的目的是研究Lipschitz映射公共不动点问题.基于传统的Ishikawa迭代和Noor迭代方法,我们引入多步Ishikawa迭代算法,并且分别给出了该算法强收敛于有限族拟-Lipschitz映射和伪压缩映射公共不动点的充分必要条件.此外,我们证明了该算法强收敛到非扩张映射的公共不动点.作为应用,我们给出数值试验证实所得的结论.     

广义线性互补问题的改进SLP算法及收敛性

考虑广义线性互补问题,提出一个求解它的改进的序列线性规划算法,并在一定条件下证得该法具有良好的收敛性质。此外,顺便给出该问题解集非空有界的一个充分条件。     

Stability of Richtmyer Type Difference Schemes in any Finite Number of Space Variables and Their Comparison with Multistep Strang Schemes

The stability of generalized Richtmyer two step difference schemesin any finite number of space variables is examined and a sufficientstability condition obtained for each scheme. In certain casesthis condition is shown to be optimal C.F.L. The efficiencyof these schemes in solving time dependent problems in two andthree space variables is examined and the schemes are seen tocompare favourably with the corresponding multistep forms ofStrang's schemes.     

多重参数算法收敛性分析

本文用分段线性函数逼近控制函数,从而将最优控制问题化为参数非线性规划我们着重讨论算法的收敛性     

混合遗传算法收敛性分析

针对遗传算法爬山能力弱但合局搜索能力强的特点 ,本文将遗传算法嵌入到基入传统优化的拟下降算法中 ,并对算法的拟下降步骤做了一定的改进 ,使得整个算法具有全局收敛性 .本文采用马尔可夫的观点进一步证明了算法的全局收敛性 ,并用极难优化的测试函数给出了数值算例 ,证明了本文算法为一种可行的全局优化算法 .     

网络路径问题及其多目标扩展形式的混合进化算法

本文就几类困难的网络路径问题及其多目标扩展形式给出相应的混合型进化算法,并在微机上予以实现,为复杂的组合优化问题提供了新的求解手段．     

An Inertial Proximal Algorithm with Dry Friction: Finite Convergence Results

Let H be a Hilbert space and A, B: H ⇉ H two maximal monotone operators. In this paper, we investigate the properties of the following proximal type algorithm:

Nonmonotone Levenberg–Marquardt Algorithms and Their Convergence Analysis

In this paper, two nonmonotone Levenberg–Marquardt algorithms for unconstrained nonlinear least-square problems with zero or small residual are presented. These algorithms allow the sequence of objective function values to be nonmonotone, which accelerates the iteration progress, especially in the case where the objective function is ill-conditioned. Some global convergence properties of the proposed algorithms are proved under mild conditions which exclude the requirement for the positive definiteness of the approximate Hessian T(x). Some stronger global convergence properties and the local superlinear convergence of the first algorithm are also proved. Finally, a set of numerical results is reported which shows that the proposed algorithms are promising and superior to the monotone Levenberg–Marquardt algorithm according to the numbers of gradient and function evaluations.     

Acceleration of Convergence of Static and Dynamic Iterations

A new technique for acceleration of convergence of static and dynamic iterations for systems of linear equations and systems of linear differential equations is proposed. This technique is based on splitting the matrix of the system in such a way that the resulting iteration matrix has a minimal spectral radius for linear systems and a minimal spectral radius for some value of a parameter in Laplace transform domain for linear differential systems.This revised version was published online in October 2005 with corrections to the Cover Date.     

Mean Convergence of Extended Lagrange Interpolation with Freud Weights

Let W := exp(-Q), where Q is of smooth polynomial growth at , for example Q(x) = |x|, > 1. We call W² a Freud weight. The mean convergence of Lagrange interpolation at the zeros of the orthonormal polynomials associated with the Freud weight WW² has been studied by several authors, as has the Lebesgue function of Lagrange interpolation. J. Szabados had the idea to add two additional points of interpolation, thereby reducing the Lebesgue constant to grow no faster than log n. In this paper, we show that mean convergence of Lagrange interpolation at this extended set of nodes displays a similar advantage over merely using the zeros of the orthogonal polynomials.     

遗传算法收敛率的下鞅分析

通过鞅论分析来给出遗传算法的收敛率 ,这种分析方法的优势在于它不依赖于染色体的编码形式如常用的二进制形式 ,也不依赖于转移矩阵及其特征值的分析 ,它只以概率来给出遗传算法的收敛率 ,在形式上更加简单明了 ,这是鞅分析优于其它分析如马尔可夫链分析的独特优势 .本文分别对在一定条件下收敛的杰出遗传算法和整体退火遗传算法给出了收敛率的概率形式o( 1- mNn · sNn)和o 1N +N0+( 2 - cN0n - mN0n)e(Δ-δ) /Tn .