一类非光滑非凸优化问题的神经网络方法

提出了解决一类带等式与不等式约束的非光滑非凸优化问题的神经网络模型。证明了当目标函数有下界时,神经网络的解轨迹在有限时间收敛到可行域。同时,神经网络的平衡点集与优化问题的关键点集一致,且神经网络最终收敛于优化问题的关键点集。与传统基于罚函数的神经网络模型不同,提出的模型无须计算罚因子。最后,通过仿真实验验证了所提出模型的有效性。     

离散时间反馈神经网络的渐近行为研究

Hopfield神经网络是一类应用非常成功的人工神经网络模型,它是研究这个反馈神经网络的基础．该文主要研究离散时间、连续状态的反馈神经网络,它是Hopfield神经网络的推广．众所周知,研究反馈神经网络的稳定性不仅被认为是神经网络最基本、最主要的问题之一,同时也是神经网络各种应用的基础．文中主要研究离散时间反馈神经网络的稳定性,给出了连接权矩阵非对称的并且输入-输出函数是一般的S-函数的新的渐近收敛性条件及相应的收敛性结论．所获结果不仅推广了一些已有的结论,而且为反馈神经网络的应用提供了一定的理论基础．     

求解线性约束二次优化问题的神经计算模型

本文提出了一种求解线性约束二次优化问题的神经模型 ,研究了该神经网络的稳定性和收敛性 ,给出了电路框图 ,并通过算例证明了该神经网络的可行性。     

一种新型暂态混沌神经网络及其在函数优化中的应用

本文提出了一种新颖的混沌神经元模型,其激励函数由Gauss函数和Sigmoid函数组成,分又图和Lyapunov指数的计算袁明其具有复杂的混沌动力学特性。在此基础上构成一种暂态混沌神经网络,将大范围的倍周期倒分叉过程的混沌搜索和最优解邻域内的类似Hopfield网络的梯度搜索相结合,应用于函数优化计算问题的求解。实验证明,它具有较
较强的全局寻优能力和较快的收敛速度。     

Subgradient-based feedback neural networks for non-differentiable convex optimization problems

1 Introduction Optimization problems arise in a broad variety of scientific and engineering applica- tions. For many practice engineering applications problems, the real-time solutions of optimization problems are mostly required. One possible and very pr…     

An energy function for the random neural network

Since Hopfield's seminal work on energy functions for neural networks and their consequence for the approximate solution of optimization problems, much attention has been devoted to neural heuristics for combinatorial optimization. These heuristics are often very time-consuming because of the need for randomization or Monte Carlo simulation during the search for solutions. In this paper, we propose a general energy function for a new neural model, the random neural model of Gelenbe. This model proposes a scheme of interaction between the neurons and not a dynamic equation of the system. Then, we apply this general energy function to different optimization problems.     

A bundle-type auxiliary problem method for solving generalized variational-like inequalities

For generalized variational-like inequalities, by combining the auxiliary principle technique with the bundle idea for nonconvex nonsmooth minimization, we present an implementable iterative method. To make the subproblem easier to solve, even though the preinvex function may not be convex, we still consider using the model similar to the one in [R. Mifflin, A modification and extension of Lemarechal’s algorithm for nonsmooth minimization, Mathematical Programming 17 (1982) 77–90] (which may not be under the preinvex function) to approximate locally the involved preinvex function, and prove that this local approximation is well defined at each iteration of the algorithm, i.e., the construction of this local approximation can terminate in finite steps at each iteration of the proposed algorithm. We not only explain how to construct the approximation, but also prove the weak convergence of the sequence generated by the corresponding algorithm under some conditions. The proposed algorithm is a generalization of the existing algorithm for generalized variational inequalities to generalized variational-like inequalities in some sense, see [T.T. Hue, J.J. Strodiot, V.H. Nguyen, Convergence of the approximate auxiliary problem method for solving generalized variational inequalities, Journal of Optimization Theory and Applications 121 (2004) 119–145].     

一种自适应构造神经网络的新方法

目前,神经网络在很多学科领域中得到广泛的应用,但是有些问题至今仍未能获得令人满意的解决方法,如何确定合适的网络结构便是其一。该文根据生物神经元状态变化导致人脑空间结构和状态变化这一原理,提出了一种自适应构造神经网络的新方法。该方法在学习过程中根据性能指标下降幅度来决定增加或减少隐含层节点数,从而起到结构优化的作用。仿真结果表明,该方法是可行的、有效的,为神经网络结构优化提供了一种新方法。     

具有非凸输入约束的不确定严格反馈系统有限时间自适应跟踪控制

针对一类具有非凸输入约束和外界干扰的不确定多输入多输出严格反馈非线性系统,提出一种有限时间自适应神经网络动态面跟踪控制方案.首先,通过引入非凸约束算子,将所设计反馈控制输入转化为与其同方向具有最大幅值的实际输入向量,进而保证实际控制输入始终保持在非凸约束集合内;然后,采用径向基神经网络逼近不确定连续函数向量,以解决控制增益矩阵上下界未知情形下的控制问题,并利用不等式放缩处理未知有界干扰;接着,利用反步法设计有限时间自适应动态面跟踪控制器,保证闭环系统所有信号均为一致最终有界的,实现期望轨迹的有限时间跟踪控制;最后,给出数值仿真算例以表明所提出控制方案的有效性.     

以高维输入神经网络作为生产线产品质量模型

探索用高维输入的神经网络对复杂工业生产过程的建模方法。针对网络输入变量维数较高的特点,提出一种ＢＰ网络各权重独立训练的分散训练方法。该方法用附加大惯性项来协调各个权重的优化训练,运用非线性优化方法调节步长。与用普通的ＢＰ训练方法相比,用该方法训练高维输入的ＢＰ网络具有较快的收敛速度和较高的模型精度,较好地解决了实际生产过程的产品质量模型问题。     

基于粒子群的TCP非凸优化速率控制算法

为了有效地解决网络中拥塞问题,针对实际网络中存在非弹性流的情况,考虑了网络中非凸优化速率控制问题。基于最大化用户效用函数框架,去掉了以往研究中对效用函数的严格假设,利用粒子群方法设计了分布式速率控制算法。算法中链路从网络获知拥塞链路的条数,用户根据对应的效用函数和拥塞反馈信息调整自身速率。仿真结果表明,算法可以很快地收敛到最优速率。     

一种新型的广义RBF神经网络及其训练方法

提出一种新型的广义RBF神经网络模型,将径向基输出权值改为权函数,采用高次函数取代线性加权.给出网络学习方法,并通过仿真分析研究隐单元宽度、权函数幂次等参数的选取对网络逼近精度以及训练时间的影响.结果表明,和传统的RBF神经网络相比,该网络具有良好的逼近能力和较快的计算速度,在系统辨识和控制中具有广阔的应用前景.     

基于遗传算法的前馈神经网络结构优化

为防止交叉后优秀基因段的丢失,在随机非一致线性交叉的基础上,设计了一种与个体适应度相关的线性交叉方案。构造了一种使交叉率与变异率随进化过程自适应调整的方法,有效抑制了遗传算法的早熟收敛。然后,针对函数逼近问题用改进后的遗传算法去优化前馈神经网络的结构,降低了神经网络训练陷入局部最优的可能性,提高了网络的泛化能力。     

基于最小二乘法的SIMO傅里叶神经网络研究

利用傅里叶级数的原理,构造单输入、多输出(SIMO)傅里叶神经网络,将非线性映射转化成为线性映射,将求解神经网络权值的方法由非线性优化方法转化成为线性优化方法,并采用最小二乘法计算网络的权值,从而大大提高了神经网络的收敛速度并避免了局部极小问题.而且,在训练输出样本受白噪声影响时,最小二乘法具有良好的降低噪声影响的功能．     

A Dual‐Type Method Based Algorithm for Nonlinear Large Network Optimization Problems

In previous research, we have proposed a Dual Projected Pseudo Quasi Newton (DPPQN) method which differs from the conventional Lagrange relaxation method by treating the inequality constraints as the domain of the primal variables in the dual function and using Projection Theory to handle the inequality constraints. We have combined this dual‐type method with a Projected Jacobi (PJ) method to solve nonlinear large network optimization problems with decomposable inequality constraints, and have achieved several attractive features. To retain the attractive features and to remedy the flaw of the previous method, in the current paper, we propose an active set strategy based DPPQN method to solve the projection problem formed by coupling functional inequality constraints. This method associated with the DPPQN method and the PJ method can be used to solve general nonlinear large network optimization problems. We present this algorithm, demonstrate its computational efficiency through numerical simulations and compare it with the previous method.     

Algebraic conditions of stability for Hopfield neural network

Using the relationship between the resistance, capacitance and current in Hopfield neural network, and the properties of sigmoid function, this paper gives the terse, explicit algebraical criteria of global exponential stability, global asymptotical stability and instability. Then this paper makes clear the essence of the stability that Hopfield defined, and provides a theoretical foundation for the design of a network.     

Nonlinear multiobjective model-predictive control scheme for wastewater treatment process

A nonlinear multiobjective model-predictive control (NMMPC) scheme, consisting of self-organizing radial basis function (SORBF) neural network prediction and multiobjective gradient optimization, is proposed for wastewater treatment process (WWTP) in this paper. The proposed NMMPC comprises a SORBF neural network identifier and a multiple objectives controller via the multi-gradient method (MGM). The SORBF neural network with concurrent structure and parameter learning is developed as a model identifier for approximating on-line the states of WWTP. Then, this NMMPC optimizes the multiple objectives under different operating functions, where all the objectives are minimized simultaneously. The solution of optimal control is based on the MGM which can shorten the solution time. Moreover, the stability and control performance of the closed-loop control system are well studied. Numerical simulations reveal that the proposed control strategy gives satisfactory tracking and disturbance rejection performance for WWTP. Experimental results show the efficacy of the proposed method.