非扩张映像不动点新的简单逼近算法

提出了一个简单的非扩张映像不动点的逼近算法,该算法通过非迭代的逼近序列来实现.从算法的复杂性来看,提出的算法比经典的Mann迭代算法、Ishikawa迭代算法和Halpern迭代算法更简单.提出的算法紧密联系着非扩张映像不动点的存在性,因此,还得到了非扩张映像的新不动点定理, 拓展和改进了经典的Goebel-Kirk,Kim-Xu等作者的结果.     

大规模多设施Weber问题的改进Cooper算法

 多设施Weber问题（multi-source Weber problem,MWP）是设施选址中的重要模型之一,而Cooper算法是求解MWP最为常用的数值方法.Cooper算法包含选址步和分配步,两步交替进行直至达到局部最优解.本文对Cooper算法的选址步和分配步分别引入改进策略,提出改进Cooper算法：选址步中将Weiszfeld算法和adaptive Barzilai-Borwein （ABB）算法结合,提出收敛速度更快的ABB-Weiszfeld算法求解选址子问题;分配步中提出贪婪簇分割策略来处理退化设施,由此进一步提出具有更好性质的贪婪混合策略.数值实验表明本文提出的改进策略有效地提高了Cooper算法的计算效率,改进算法有着更好的数值表现.     

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.     

高阶PageRank问题的一个两步分裂迭代算法

在一般PageRank问题的基础上,Gleich等结合了马尔科夫链的性质提出了高阶PageRank问题.基于Gleich等提出的几个算法,结合两步分裂迭代的思想提出了解高阶PageRank问题的一个两步分裂迭代算法.该算法能增加收敛的范围,并且减少算法的迭代步数.     

非精确信赖域类型算法及收敛性分析

在求解大规模数据的优化问题时,由于数据规模和维数较大,传统的算法效率较低.本文通过采用非精确梯度和非精确Hessian矩阵来降低计算成本,提出了非精确信赖域算法和非精确自适应三次正则化算法.在一定条件下,证明了算法有限步停止,并估计了算法迭代的复杂度.特别地,我们分析了采用随机抽样时算法在给定概率下的复杂度.最后,通过二分类问题的数值求解,比较了本文提出的随机信赖域算法,随机自适应三次正则化算法和已有算法收敛效率.数值结果表明在相同精度下,本文提出的算法效率更高,并且随机自适应三次正则化算法的效率优于随机信赖域算法.     

一种求解非线性鞍点问题的交替投影方法

本文针对一类连续非线性Max-Min优化所对应的鞍点问题,提出了一种交替投影算法,证明了算法的收敛性.初步的数值实验表明本文所提出的算法比已有的同类算法具有更高的计算效率.     

一种快速且全局收敛的BP神经网络学习算法

目前误差反向传播(BP)算法在训练多层神经网络方面有很多成功的应用.然而,BP算法也有一些不足:收敛缓慢和易陷入局部极小点等.提出一种快速且全局收敛的BP神经网络学习算法,并且对该优化算法的全局收敛性进行分析和详细证明.实证结果表明提出的算法比标准的BP算法效率更高且更精确.     

灵活单纯形算法

本文概述C.B.Garcia和W.I.Zangwill的灵活单纯形算法,论证算法的可行性,并对在优化问题中应用灵活单纯形算法的前景进行探讨。 1.引言自从Scarf首先利用Lemke、Lemke和Howson的互补原理来计算非线性映射不动点以来,许多求不动点或零点的算法出现了。例如:Merrill提出的重复开始算法,Kuhn和Mackinnon提出的“三明治”算法,Eaves提出的单纯同伦算法等等。     

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.     

广义超立方体网络的寻径算法

利用H amm ing距离概念,在广义超立方体中的点对之间提出两个基于H amm ing距离的确定性寻径算法—算法1、算法2,分析了这两种算法的特点.为了克服确定性寻径算法易出现的通道拥挤现象,文中提出了一种自适应算法—算法3.     

Global convergence of a modified limited memory BFGS method for non-convex minimization

In this paper, a modified limited memory BFGS method for solving large-scale unconstrained optimization problems is proposed. A remarkable feature of the proposed method is that it possesses global convergence property without convexity assumption on the objective function. Under some suitable conditions, the global convergence of the proposed method is proved. Some numerical results are reported which illustrate that the proposed method is efficient.     

解凸约束非线性单调方程组的无导数谱PRP投影算法

本文在著名PRP共轭梯度算法的基础上研究了一种无导数谱PRP投影算法,并证明了算法在求解带有凸约束条件的非线性单调方程组问题的全局收敛性.由于无导数和储存量小的特性,它更适应于求解大规模非光滑的非线性单调方程组问题.数值试验表明,新算法对给定的测试问题是有效的和稳定的.     

An Optimal Extension of the Polak–Ribière–Polyak Conjugate Gradient Method

Based on a singular value analysis on an extension of the Polak–Ribière–Polyak method, a nonlinear conjugate gradient method with the following two optimal features is proposed: the condition number of its search direction matrix is minimum and also, the distance of its search direction from the search direction of a descent nonlinear conjugate gradient method proposed by Zhang et al. is minimum. Under proper conditions, global convergence of the method can be achieved. To enhance e?ciency of the proposed method, Powell’s truncation of the conjugate gradient parameters is used. The method is computationally compared with the nonlinear conjugate gradient method proposed by Zhang et al. and a modified Polak–Ribière–Polyak method proposed by Yuan. Results of numerical comparisons show e?ciency of the proposed method in the sense of the Dolan–Moré performance profile.     

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．     

Simultaneous estimation of thin film thickness and optical properties using two-stage optimization

In this work, we proposed the new method for estimation of the thickness and the optical properties of the thin metal oxide film deposited on a transparent substrate. The developed method uses only transmittance spectra measured. Our method is based on the two stage optimization where the thickness is determined in the outer stage and the optical properties are determined in the inner stage. The differential evolutionary algorithm is used in solving the formulated problem. The proposed method was illustrated in the case study of Titanium dioxide film deposited on a glass substrate. The results indicate that the thickness and the optical properties estimated agree well with the experiment. Moreover, we investigated robustness of the proposed method in the case of transmittance spectra containing noises. The data were modelled by adding random noises ranging between 0 and 30% to the transmittance spectra measured. It is seen that the proposed method has better robustness and performance than the existing method based on pointwise unconstrained minimization approach. In solving the estimation problem, the performance of the proposed method was also compared with the well-known Levenberg?CMarquardt method and single stage differential evolutionary method. The results indicate that the proposed method has better performance than Levenberg?CMarquardt method and single stage differential evolutionary method. Moreover, the proposed method is more robust to random noise than Levenberg?CMarquardt method and single stage differential evolutionary method.     

可分离凸优化问题的非精确平行分裂算法

针对一类可分离凸优化问题提出了一种非精确平行分裂算法.该算法充分利用了所求解问题的可分离结构,并对子问题进行非精确求解.在适当的条件下,证明了所提出的非精确平行分裂算法的全局收敛性,初步的数值实验说明了算法有效性.     

A generalized crossing local search method for solving vehicle routing problems

In this paper, we propose a generalized crossing local search method for solving vehicle routing problems. This method is a generalization of the string crossing method described in the literature. To evaluate the performance of the proposed method, extensive computational experiments on the proposed method applied to a set of benchmark problems are carried out. The results show that the proposed method, when coupled with metaheuristics such as simulated annealing, is comparable with other efficient heuristic methods proposed in the literature.     

A Switching Algorithm Based on Modified Quasi-Newton Equation

In this paper, a switching method for unconstrained minimization is proposed. The method is based on the modified BFGS method and the modified SR1 method. The eigenvalues and condition numbers of both the modified updates are evaluated and used in the switching rule. When the condition number of the modified SR1 update is superior to the modified BFGS update, the step in the proposed quasi-Newton method is the modified SR1 step. Otherwise the step is the modified BFGS step. The efficiency of the proposed method is tested by numerical experiments on small, medium and large scale optimization. The numerical results are reported and analyzed to show the superiority of the proposed method.     

Piecewise shooting reproducing kernel method for linear singularly perturbed boundary value problems

In this letter, a new numerical method is proposed for solving second order linear singularly perturbed boundary value problems with left layers. Firstly a piecewise reproducing kernel method is proposed for second order linear singularly perturbed initial value problems. By combining the method and the shooting method, an effective numerical method is then proposed for solving second order linear singularly perturbed boundary value problems. Two numerical examples are used to show the effectiveness of the present method.     

非线性l1问题的光滑近似算法

为非线性l1问题的求解构造了光滑逼近函数.首先将非线性l1问题转化为等价的不可微优化问题;其次通过两步提出光滑逼近函数的一般性构造方法;最后进行了数值仿真.文中介绍了光滑逼近函数的有关性质,指出相关文献已有的光滑函数方法是本文的特例,并证明了方法的收敛性及有效性.