投影型神经网络算法的全局收敛性分析

投影型神经网络具有自然保证解的可行性、可调参数少、搜索方向维数低和模型结构简单等优点,已引起众多学者关注．神经网络可用于求解优化问题的前提是它应具有全局收敛性．目前,该模型的这一性质仅对有界约束下严格凸二次规划问题得到了证明．该文利用常微分方程理论和LaSalle不变原理,通过构造Lyapunov函数,证明了该网络对一般凸规划问题的全局收敛性,并将约束区域推广到任一闭凸集．该文的结论奠定了该类网络的应用基础,扩大了它的应用范围．同时作者也讨论了该模型在较弱限制条件下的指数收敛性．最后给出一组实例,说明该网络计算上是可行和有效的．     

求解互补支持向量机的非单调信赖域算法

求解支持向量机的核心问题是对一个大规模凸二次规划问题进行求解。基于支持向量机的修正模型,得到一个与之等价的互补问题,利用Fischer-Burmeister互补函数,从一个新的角度提出了求解互补支持向量机的非单调信赖域算法。新算法避免了求解Hesse矩阵或矩阵求逆运算,减少了工作量,提高了运算效率。在不需要任何假设的情况下,证明算法具有全局收敛性。数值实验结果表明,对于大规模非线性分类问题,该算法的运行速度比LSVM算法和下降法快,为求解SVM优化问题提供了一种新的可行方法。     

赋权图匹配问题的一种新的松弛模型

图匹配是一个NP难(NP-hard)问题. 基于置换矩阵是非负正交矩阵这一经典结论, 提出赋权图匹配(Weighted graph matching, WGM)的双向松弛障碍规划, 理论上证明新模型的解与原模型的解是一致的. 该规划是一个二元连续规划, 它是正交矩阵上的线性优化问题, 同时也是非负矩阵上的凸二次优化问题. 故设计求解新模型的交替迭代算法, 并证明算法的局部收敛性. 数值实验表明, 在匹配精度方面, 新方法强于线性规划方法和特征值分解方法.     

基于乘性规则的支持向量机

传统的二次规划由于涉及大量的矩阵运算，运算速度慢成为支持向量机的最大缺点．已有的乘性规则仅适于非负二次凸规划问题，推导出了求解支持向量机中混合约束二次凸规划的乘性规则，利用这一乘性规则极大地提高了优化速度．该方法提供了一种直接优化的方法，其所有变量可以并行迭代，乘性规则可以使得二次规划的目标函数单调下降到它的全局最小点．仿真试验结果表明了该算法有效性．     

梯度神经网络解线性矩阵方程之收敛性分析

为了求解线性矩阵方程问题,应用一种基于负梯度法的递归神经网络模型,并探讨了该递归神经网络实时求解线性矩阵方程的全局指数收敛问题.在讨论渐近收敛性基础上,进一步证明了该类神经网络在系数矩阵满足有解条件的情况下具有全局指数收敛性,在不能满足有解条件的情况下具有全局稳定性.计算机仿真结果证实了相关理论分析和该网络实时求解线性矩阵方程的有效性.     

Aug-PDG: 带不等式约束凸优化算法的线性收敛性

原始-对偶梯度算法广泛应用于求解带约束的凸优化问题, 大部分文献仅证明了该算法的收敛性, 而没有分析其收敛速度. 因此, 本文研究了求解带有不等式约束凸优化的一类离散算法, 即增广原始-对偶梯度算法 (Aug-PDG), 证明了Aug-PDG 算法在一些较弱的假设条件下可以半全局线性收敛到最优解, 并明确给出了算法中步长的上界. 最后, 数值算例证实了所得理论结果的有效性.     

有限元大型二次规划解的一种新算法

１．引言工程中许多优化问题可导致求解一个标准或非标准的二次规划问题．经典的Ｌｅｍｋｅ图表算法对中、小型规模的问题,具有稳定性及收敛性好的特点,被广泛应用．对于大型规模的题目,一方面由于矩阵本身的问题难于保证有较好的数值稳定性,另一方面大型矩阵的消元换基运算要导致较大的计算工作量,因此,针对具体大类问题提供高效的算法是必要的．参变量变分原理较好地解决了塑性力学、接触力学等经典变分法难于适应的问题．运用线性化手段削弱了约束方程的非线性程度,将问题转化为一个有线性互补显式条件的二次凸泛函极值求解,并利…     

基于序列二次规划的非线性不等式状态约束滤波算法

针对非线性不等式状态约束滤波问题,提出一种基于序列二次规划的迭代不敏卡尔曼滤波算法。在迭代不敏卡尔曼滤波的基础上,采用序列二次规划优化法求解非线性不等式约束条件下的最优解。通过对每一次迭代求解二次规划子问题来确定下降方向,重复该步骤直到求得原问题的解,利用效益函数对目标函数最小化和不等式约束条件进行权衡,以保证算法的收敛性,利用正定矩阵近似海森矩阵降低时间复杂度。对具有约束的航路跟踪系统进行实验仿真,结果表明,该算法在处理非线性不等式状态约束滤波问题时,能够有效地提高状态估计精度,获得较高的滤波精度,且时间复杂度较低。     

一种修正的Cauchy-Barzilai-Borwein算法

高效率求解无约束二次凸优化问题是优化算法设计的重要任务.针对这类问题,本文提出了一种修正的Cauchy-Barzilai-Borwein算法,简称为MCBB算法.文章证明了MCBB算法对于无约束二次严格凸优化问题具有全局收敛和Q-线性收敛速率.初步的数值对比实验表明,对于坏条件问题,MCBB算法比CBB与BB算法更为有效.     

一种求解混合整数非线性规划问题的模拟退火算法

通过适当处理离散变量，将求解无约束非凸ＮＬＰ问题的高效模拟退火全局优化算法推广到求解一般非凸混合整数非线性规划问题。数值计算结果表明，文中模拟退火算法在适用性、解的质量和计算效率等方面优于其它方法，是求解一般非凸ＭＩＮＬＰ问题的一种有效的全局优化算法。     

Robust stability of delayed reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales

In this paper, the global robust exponential stability of equilibrium solution to delayed reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales is studied. Using topological degree theory, M-matrix method, Lyapunov functional and inequality skills, we establish some sufficient conditions for the existence, uniqueness and global robust exponential stability of equilibrium solution to delayed reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales. One example is given to illustrate the effectiveness of our results.     

Global Exponential Stability and Global Convergence in Finite Time of Neural Networks with Discontinuous Activations

In this paper, we consider a general class of neural networks, which have arbitrary constant delays in the neuron interconnections, and neuron activations belonging to the set of discontinuous monotone increasing and (possibly) unbounded functions. Based on the topological degree theory and Lyapunov functional method, we provide some new sufficient conditions for the global exponential stability and global convergence in finite time of these delayed neural networks. Under these conditions the uniqueness of initial value problem (IVP) is proved. The exponential convergence rate can be quantitatively estimated on the basis of the parameters defining the neural network. These conditions are easily testable and independent of the delay. In the end some remarks and examples are discussed to compare the present results with the existing ones.     

Global exponential stability analysis of delayed Cohen--Grossberg neural networks with distributed delays

In this article, the global exponential stability problem of Cohen--Grossberg neural networks with both discrete-time delays and distributed delays is investigated. The existence and global stability for the unique equilibrium of the Cohen--Grossberg neural networks with distributed delays are achieved by using some new Lyapunov functionals, M-matrix theory and some analytic techniques, and some less restrictive conditions are obtained. An example is also worked out to validate the advantages of our results.     

Stability of Reaction-Diffusion Recurrent Neural Networks with Distributed Delays and Neumann Boundary Conditions on Time Scales

The existence of equilibrium solutions to reaction-diffusion recurrent neural networks with distributed delays and Neumann boundary conditions on time scales is proved by the topological degree theory and M-matrix method. Under some sufficient conditions, we obtain the uniqueness and global exponential stability of equilibrium solution to reaction-diffusion recurrent neural networks with distributed delays and Neumann boundary conditions on time scales by constructing suitable Lyapunov functional and inequality skills. Two examples are given to illustrate the effectiveness of our results.     

Global exponential stability analysis for a class of neural networks with time delays

Employing Brouwer's fixed point theorem, matrix theory, we made a further investigation of a class of neural networks with delays in this paper. A family of sufficient conditions were given for checking global exponential stability. These results have important leading significance in the design and applications of globally stable neural networks with delays. Our results extended and improved some earlier publications. Copyright © 2011 John Wiley & Sons, Ltd.     

Stability Analysis of Periodic Solution for a Complex‐valued Neural Networks With Bounded and Unbounded Delays

This paper is devoted to investigating a class of complex‐valued neural networks with bounded and unbounded delays. By means of Mawhin's continuation theorem, some criteria on existence and uniqueness of periodic solution are established for the complex‐valued neural networks. By constructing an appropriate Lyapunov‐Krasovskii functional and M?matrix theory, some sufficient conditions are derived for the global exponential stability of periodic solutions to the complex‐valued neural networks. Finally, two numerical examples are given to show the effectiveness and merits of the present results.     

Periodic oscillation of discrete-time bidirectional associative memory neural networks

In this paper, a discrete-time bidirectional associative memory neural networks model is considered. By employing the theory of coincidence degree and using Halanay-type inequality technique we give some sufficient conditions ensuring the existence and globally exponential stability of periodic solutions for the discrete-time bidirectional neural networks. An example with the numerical simulations is provided to show the correctness of our analysis.     

Global asymptotic stability of neural networks with transmission delays

The problem of stability of the equilibrium of a class of neural networks with transmission delays is studied using the Lyapunov functional method and combining with the method of inequality analysis. Some sufficient conditions for global asymptotic stability of neural networks with transmission delays, which do not require symmetry of the connection matrix and nonlinear properties for neural units to be continuously differentiable or strictly monotonic increasing, are obtained. These conditions can be used to design globally stable networks and thus have important significance in both theory and applications. In addition, we give some examples to illustrate the main results.     

Global Exponential Stability and Existence of Periodic Solution of Impulsive Cohen–Grossberg Neural Networks with Distributed Delays on Time Scales

On time scales, by using the continuation theorem of coincidence degree theory, M-matrix theory and constructing some suitable Lyapunov functions, some sufficient conditions are obtained for the existence and exponential stability of periodic solutions of impulsive Cohen–Grossberg neural networks with distributed delays, which are new and complement of previously known results. Finally, an example is given to illustrate the effectiveness of our main results.     

Novel criteria for global robust exponential stability of neural networks with time-varying delays via LMI approach

The article addresses the problem of global robust exponential stability of interval neural networks with time-varying delays. On the basis of linear matrix inequality technique and M-matrix theory, some novel sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for delayed interval neural networks are presented. It is shown that our results improve and generalize some previously published ones. Some numerical examples and simulations are given to show the effectiveness of the obtained results.