非对称线性方程组的二阶段分裂迭代法

本文针对非对称正定矩阵提出了一个收敛分裂, 给出了分裂收敛的充要条件. 在此基础上, 提出系数为非对称正定矩阵的线性方程组的二阶段算法, 并讨论了算法的收敛条件. 最后, 通过数值例子展示了算法的有效性.     

基于正余双弦自适应灰狼优化算法的医药物流配送路径规划

针对传统灰狼优化算法易早熟收敛陷入局部最优和收敛速度慢的缺陷,提出一种正余双弦自适应灰狼优化算法.首先,在灰狼捕食阶段引入正弦搜索,增强算法的全局勘探能力,减少算法的搜索盲点,提高算法的搜索精度.在引入正弦搜索的同时,引入余弦搜索,增强算法的局部开发能力,提高算法的收敛速度.其次,在搜索过程中加入自适应交叉变异机制,通过适应度值的大小自适应选取交叉变异概率,有效的提高了粒子跳出局部最优的概率.通过数值对比试验,验证了改进算法具有较强的收敛精度和收敛速度.     

一种改进的自适应遗传算法

针对IAGA自适应遗传算法存在的未成熟收敛问题,提出了一种改进的自适应遗传算法(NIAGA算法),根据自定义判别式判断群体是否出现了未成熟收敛趋势,由不同情况,分别采用宏观调控与微观处理两种方法来设置交叉概率Pc和变异概率Pm,以此促使算法摆脱未成熟收敛.仿真结果表明,新算法有效地改善了IAGA算法的未成熟收敛问题,显示出了更强的全局收敛性.     

一种新的双模式盲均衡算法研究

针对恒模算法(CMA)收敛速度较慢、收敛后均方误差较大的缺点,提出一种新的双模式盲均衡算法.在算法初期,利用能快速收敛的归一化恒模算法(NCMA)进行冷启动,在算法收敛后切换到判决引导(DD-LMS)算法,减少误码率.计算机仿真表明,提出的新算法有较快的收敛速度和较低的误码率.     

弱相对非扩张映像不动点单调CQ算法与应用

Kamimura和Takahashi$^{[7]}$证明了相对非扩张映像CQ迭代算法的强收敛定理.该文构造了单调CQ算法, 用来逼近弱相对非扩张映像不动点, 证明了强收敛定理. 并将结果应用于逼近Banach空间极大单调算子的零点. 单调CQ算法比目前的CQ算法收敛速度快. 另外, 为证明弱相对非扩张映像不动点强收敛定理,该文运用了新的Cauchy列证明方法, 而不用Kadec-Klee性质, 该文结果改进了S.Matsushita 和 W.Takahashi及其它人的结果.     

一种改进的FastICA算法

FastICA算法是一种快速独立分量分析(Independent Component Analysis:ICA)算法,但它是基于牛顿迭代方法和合理近似的一种算法,所以具有改进空间.近年来提出了许多改进的具有更高阶收敛性质的牛顿迭代方法.将一种3阶收敛的牛顿迭代方法引入ICA算法的推导中,在合理近似的基础上,提出了一种改进的两步迭代FastICA算法.与传统FastICA算法相比,提出的改进的FastICA算法一次迭代的计算量有所增加.但是,实验结果表明,新提出的改进的FastICA算法更稳健、具有更快的收敛速度.     

自适应间断Galerkin 有限元的多水平方法

本文讨论在自适应网格上间断Galerkin 有限元离散系统的局部多水平算法. 对于光滑系数和间断系数情形, 利用Schwarz 理论分析了算法的收敛性. 理论和数值试验均说明算法的收敛率与网格层数以及网格尺寸无关. 对强间断系数情形算法是拟最优的, 即收敛率仅与网格层数有关.     

具有非平稳相关输入的自适应阵算法

在输入{X_k} 是相互独立的平稳随机序列的假定下,自适应阵算法的收敛性问题得到较好的解决.当目标信号Y(t)的某些统计特性已知时,给出了问题的解.当我们对目标信号一无所知时,用对加权阵施加约束的方法来代替,也证明了算法的期望收敛于最优解.修改了这一算法,并进一步证明了算法期望收敛、几乎处处收敛和均方收敛于最优解.则综合了上述方法,并取消了对输入协方差阵R=EX_kX_k~T和约束条件阵C~τC是非奇异的要求,而给出了一个使用范围更广的算法.也证明了算法几     

基于云自适应遗传算法的K-means聚类分析

现有的基于遗传算法的K-means聚类算法,利用遗传算法的全局优化性提高了K-means算法的寻优能力,收敛速度却过慢.为了解决上述问题,提出基于云自适应遗传算法的K-means聚类算法,利用云模型云滴的随机性和稳定趋向性设计遗传算法的交叉和变异概率,并在进化过程中引入K均值算子,以克服算法收敛速度过慢的问题.实验比较表明,算法具有较好的全局优化性,且收敛速度较快,提高了聚类算法解决物流管理中数据聚类工作的能力.     

求解非线性方程组的一种新的全局收敛的Levenberg-Marquardt算法

本文提出了求解非线性方程组的一种新的全局收敛的Levenberg-Marquardt算法,即μk=ακ(θ||F_k|| (1-θ)||J_k~TF_k||),θ∈[0,1],其中ακ利用信赖域技巧来修正.在不必假设雅可比矩阵非奇异的局部误差界条件下,证明了该算法是全局收敛和局部二次收敛的.数值试验表明该算法能有效地求解奇异非线性方程组问题.     

线性二阶锥互补问题的一种非精确光滑算法

在光滑算法的框架下,就线性二阶锥互补问题,给出了一种非精确光滑算法. 在适当的条件下,证明了该算法具有全局收敛性. 数值试验表明该算法对高维线性二阶锥互补问题是有效的.     

Nonmonotone smoothing Broyden-like method for generalized nonlinear complementarity problems

Based on a new symmetrically perturbed smoothing function, the generalized nonlinear complementarity problem defined on a polyhedral cone is reformulated as a system of smoothing equations. Then we suggest a new nonmonotone derivative-free line search and combine it into the smoothing Broyden-like method. The proposed algorithm contains the usual monotone line search as a special case and can overcome the difficult of smoothing Newton methods in solving the smooth equations to some extent. Under mild conditions, we prove that the proposed algorithm has global and local superlinear convergence. Furthermore, the algorithm is locally quadratically convergent under suitable assumptions. Preliminary numerical results are also reported.     

Hyperbolic smoothing function method for minimax problems

In this article, an approach for solving finite minimax problems is proposed. This approach is based on the use of hyperbolic smoothing functions. In order to apply the hyperbolic smoothing we reformulate the objective function in the minimax problem and study the relationship between the original minimax and reformulated problems. We also study main properties of the hyperbolic smoothing function. Based on these results an algorithm for solving the finite minimax problem is proposed and this algorithm is implemented in general algebraic modelling system. We present preliminary results of numerical experiments with well-known nonsmooth optimization test problems. We also compare the proposed algorithm with the algorithm that uses the exponential smoothing function as well as with the algorithm based on nonlinear programming reformulation of the finite minimax problem.     

A predictor-corrector smoothing Newton method for symmetric cone complementarity problems

In this paper, we present a predictor-corrector smoothing Newton method for solving nonlinear symmetric cone complementarity problems (SCCP) based on the symmetrically perturbed smoothing function. Under a mild assumption, the solution set of the problem concerned is just nonempty, we show that the proposed algorithm is globally and locally quadratic convergent. Also, the algorithm finds a maximally complementary solution to the SCCP. Numerical results for second order cone complementarity problems (SOCCP), a special case of SCCP, show that the proposed algorithm is effective.     

A smoothing Newton algorithm for solving the monotone second-order cone complementarity problems

In this paper, a new smoothing function is given by smoothing the symmetric perturbed Fischer-Burmeister function. Based on this function, a smoothing Newton algorithm is proposed for solving the monotone second-order cone complementarity problems. The global and local quadratic convergence results of the algorithm are established under suitable assumptions. The theory of Euclidean Jordan algebras is a basic tool which is extensively used in our analysis. Numerical results indicate that the proposed algorithm is effective.     

非线性互补约束规划问题的一个新的QP-free算法

本文研究了非线性互补约束均衡问题.利用互补函数以及光滑近似法,把非线性互补约束均衡问题转化为一个光滑非线性规划问题,得到了超线性收敛速度,数值实验结果表明本文提出的算法是可行的.     

Non-parametric kernel regression for multinomial data

This paper presents a kernel smoothing method for multinomial regression. A class of estimators of the regression functions is constructed by minimizing a localized power-divergence measure. These estimators include the bandwidth and a single parameter originating in the power-divergence measure as smoothing parameters. An asymptotic theory for the estimators is developed and the bias-adjusted estimators are obtained. A data-based algorithm for selecting the smoothing parameters is also proposed. Simulation results reveal that the proposed algorithm works efficiently.     

A family of new smoothing functions and?a?nonmonotone smoothing Newton method for?the?nonlinear complementarity problems

In this paper, based on a p-norm with p being any fixed real number in the interval (1,+??), we introduce a family of new smoothing functions, which include the smoothing symmetric perturbed Fischer function as a special case. We also show that the functions have several favorable properties. Based on the new smoothing functions, we propose a nonmonotone smoothing Newton algorithm for solving nonlinear complementarity problems. The proposed algorithm only need to solve one linear system of equations. We show that the proposed algorithm is globally and locally superlinearly convergent under suitable assumptions. Numerical experiments indicate that the method associated with a smaller p, for example p=1.1, usually has better numerical performance than the smoothing symmetric perturbed Fischer function, which exactly corresponds to p=2.     

A smoothing Newton method for second-order cone optimization based on a new smoothing function

A new smoothing function is given in this paper by smoothing the symmetric perturbed Fischer-Burmeister function. Based on this new smoothing function, we present a smoothing Newton method for solving the second-order cone optimization (SOCO). The method solves only one linear system of equations and performs only one line search at each iteration. Without requiring strict complementarity assumption at the SOCO solution, the proposed algorithm is shown to be globally and locally quadratically convergent. Numerical results demonstrate that our algorithm is promising and comparable to interior-point methods.