具有变时滞和马尔可夫切换的随机递归神经网络的弱收敛(英文)

本文研究了具有变时滞和马尔可夫切换的随机递归神经网络的弱收敛,通过运用Lyapunov函数、随机分析技巧和推广了的Halanay不等式,得到了上述模型为弱收敛的充分性条件,并且我们揭示了对上述递归神经网络模型所确定的segment过程的转移概率的极限分布是此模型的解过程的唯一的遍历不变概率测度.此外,我们还给出了例子和数值模拟来说明我们结论的正确性.     

无界延迟随机微分方程一般衰减速度的稳定性（英文）

本文用Lyapunov函数技巧对非线性无界延迟随机微分方程建立整体解的存在唯一性定理.利用半鞅收敛定理,研究零解的一般衰减速度的随机稳定性并给出判定定理.     

具S-型分布时滞的细胞神经网络的概周期解

该文研究一类具S-型分布时滞的细胞神经网络(CNNs)的概周期解及全局指数型稳定性问题.利用指数型二分性和Schauder不动点定理以及构造Lyapunov函数,得到了细胞神经网络模型概周期解和指数稳定性的一些充分条件.此外,给出一个实例说明结果是可行的.     

具有脉冲的高阶时滞Hopfield神经网络的全局指数稳定性

高阶Hopfield神经网络可以看作是Hopfield神经网络的扩展,相对一阶神经网络而言,高阶神经网络在存储能力、逼近能力、容错水平和收敛速度等方面具有更强大的能力.利用构造合适的Lyapunov泛函,应用不等式性质,研究了一类具有脉冲的高阶时滞Hopfield神经网络的动力学行为,得到了确保该系统的平衡点全局指数稳定的充分判别条件.通过两个仿真例子,说明所得结论的有效性.     

具S-型分布时滞的模糊细胞神经网络的周期解及指数稳定性

研究了一类具S-型分布时滞的模糊细胞神经网络(FCNN)的周期解及全局指数稳定性问题.在不要求激励函数全局L ipsch itz条件下,通过使用指数型二分性和Schauder不动点定理以及构造Lyapunov函数,得到了模糊细胞神经网络模型周期解和指数稳定性的一些充分条件.此外,给出一个实例说明结果是可行的.     

无界可变延迟随机神经网络的指数稳定性（英文）

本文用Lyapunov函数方法和半鞅收敛定理研究无界可变延迟随机神经网络的指数稳定性.给出判定零解的均方指数稳定性和几乎必然稳定性的充分条件.本文所用的方法和结果适用于无界延迟系统,涵盖了已有文献中有界延迟系统的结果.     

具有分布时滞的非自治Cohen-Grossberg神经网络稳定性研究

对具有分布时滞的非自治Cohen-Grossberg神经网络进行了研究.通过构造适当的Lyapunov函数,利用不等式分析方法,引入多参数,得到了一系列解的一致有界性且最终有界性和全局指数稳定性的判别准则.     

一类具有混合时滞网络的渐近稳定性分析

讨论具有混合延时的T-S模糊C-G神经网络模型.通过构造一个适当的Lyapunov泛函,使用LIM矩阵不等式的技术,得到了一个保证具有混合延时T-S模糊C-G神经网络全局渐近稳定的充分条件.     

Cohen-Grossberg神经网络的全局指数稳定性分析

本文研究了CohenGrossberg神经网络模型的指数稳定性.为避免构造Lyapunov函数的困难,我们采用广义相对Dalquist数方法来分析神经网络的稳定性.借助这一方法,我们不但得到了CohenGrossberg神经网络模型平衡解的存在性、唯一性和全局指数稳定性的新的充分条件,而且给出了神经网络的指数衰减估计.所获结论改进了已有文献的相关结果.     

Caputo分数阶时滞细胞神经网络的稳定性分析

研究了一类Caputo分数阶时滞细胞神经网络模型的稳定性.通过利用分数阶微积分中的常数变分法,得到了Caputo分数阶时滞细胞神经网络解的差分形式,推导出模型的有界解和平衡点的存在性与唯一性,最后证明了神经网络的全局指数稳定性.     

Neural networks for solving second-order cone constrained variational inequality problem

In this paper, we consider using the neural networks to efficiently solve the second-order cone constrained variational inequality (SOCCVI) problem. More specifically, two kinds of neural networks are proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of the SOCCVI problem. The first neural network uses the Fischer-Burmeister (FB) function to achieve an unconstrained minimization which is a merit function of the Karush-Kuhn-Tucker equation. We show that the merit function is a Lyapunov function and this neural network is asymptotically stable. The second neural network is introduced for solving a projection formulation whose solutions coincide with the KKT triples of SOCCVI problem. Its Lyapunov stability and global convergence are proved under some conditions. Simulations are provided to show effectiveness of the proposed neural networks.     

A novel neural network based on NCP function for solving constrained nonconvex optimization problems

This article presents a novel neural network (NN) based on NCP function for solving nonconvex nonlinear optimization (NCNO) problem subject to nonlinear inequality constraints. We first apply the p‐power convexification of the Lagrangian function in the NCNO problem. The proposed NN is a gradient model which is constructed by an NCP function and an unconstrained minimization problem. The main feature of this NN is that its equilibrium point coincides with the optimal solution of the original problem. Under a proper assumption and utilizing a suitable Lyapunov function, it is shown that the proposed NN is Lyapunov stable and convergent to an exact optimal solution of the original problem. Finally, simulation results on two numerical examples and two practical examples are given to show the effectiveness and applicability of the proposed NN. © 2015 Wiley Periodicals, Inc. Complexity 21: 130–141, 2016     

A capable neural network model for solving the maximum flow problem

This paper presents an optimization technique for solving a maximum flow problem arising in widespread applications in a variety of settings. On the basis of the Karush–Kuhn–Tucker (KKT) optimality conditions, a neural network model is constructed. The equilibrium point of the proposed neural network is then proved to be equivalent to the optimal solution of the original problem. It is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the maximum flow problem. Several illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper.     

Solving a class of geometric programming problems by an efficient dynamic model

In this paper, a neural network model is constructed on the basis of the duality theory, optimization theory, convex analysis theory, Lyapunov stability theory and LaSalle invariance principle to solve geometric programming (GP) problems. The main idea is to convert the GP problem into an equivalent convex optimization problem. A neural network model is then constructed for solving the obtained convex programming problem. By employing Lyapunov function approach, it is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the original problem. The simulation results also show that the proposed neural network is feasible and efficient.     

A double projection algorithm for multi-valued variational inequalities and a unified framework of the method

In this paper, we propose a double projection algorithm for a generalized variational inequality with a multi-valued mapping. Under standard conditions, our method is proved to be globally convergent to a solution of the variational inequality problem. Moreover, we present a unified framework of projection-type methods for multi-valued variational inequalities. Preliminary computational experience is also reported.     

Strict Feasibility for Generalized Mixed Variational Inequality in Reflexive Banach Spaces

The purpose of this paper is to investigate the nonemptiness and boundedness of solution set for a generalized mixed variational inequality with strict feasibility in reflexive Banach spaces. A concept of strict feasibility for the generalized mixed variational inequality is introduced, which recovers the existing concepts of strict feasibility for variational inequalities and complementarity problems. By using the equivalence characterization of nonemptiness and boundedness of the solution set for the generalized mixed variational inequality due to Zhong and Huang (J. Optim. Theory Appl. 147:454–472, 2010), it is proved that the generalized mixed variational inequality problem has a nonempty bounded solution set is equivalent to its strict feasibility.     

Well-posedness of generalized mixed variational inequalities,inclusion problems and fixed-point problems

We introduced and studied the concept of well-posedness to a generalized mixed variational inequality. Some characterizations are given. Under suitable conditions, we prove that the well-posedness of the generalized mixed variational inequality is equivalent to the well-posedness of the corresponding inclusion problem. We also discuss the relations between the well-posedness of the generalized mixed variational inequality and the well-posedness of the corresponding fixed-point problem. Finally, we derive some conditions under which the generalized mixed variational inequality is well-posed.     

Variational inclusions for contingent derivative of set-valued maps

In this paper, we give two versions of Ky Fan's inequality for set-valued maps acting between normed vector spaces and we consider sufficient conditions to solve a variational inclusion problem concerning derivatives of set-valued maps. A selection result for set-valued maps between finite dimensional vector spaces and its contingent derivative is obtained as well; from this result we derive some conditions for the existence of a solution of a generalized variational inequality problem.     

Solvability of Generalized Variational Inequality Problems for Unbounded Sets in Reflexive Banach Spaces

By employing the notion of exceptional family of elements, we establish some existence results for generalized variational inequality problems in reflexive Banach spaces provided that the mapping is upper sign-continuous. We show that the nonexistence of an exceptional family of elements is a necessary condition for the solvability of the dual variational inequality. For quasimonotone variational inequalities, we present some sufficient conditions for the existence of strong solutions. For the pseudomonotone case, the nonexistence of an exceptional family of elements is proved to be an equivalent characterization of the problem having strong solutions. Furthermore, we establish several equivalent conditions for the solvability for the pseudomonotone case. As a byproduct, a quasimonotone generalized variational inequality is proved to have a strong solution if it is strictly feasible. Moreover, for the pseudomonotone case, the strong solution set is nonempty and bounded if it is strictly feasible.     

Lower Semicontinuity of the Solution Map to a Parametric Generalized Variational Inequality in Reflexive Banach Spaces

This paper is concerned with the study of solution stability of a parametric generalized variational inequality in reflexive Banach spaces. Under the requirements that the operator of a unperturbed problem is of class (S)_?+? and operators under consideration are pseudo-monotone and demicontinuous, we show that the solution map of a parametric generalized variational inequality is lower semicontinuous. The obtained results are proved without conditions related to the degree theory and the metric projection.