一类广义变分不等式问题的神经网络模型
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摘要
基于解的充分必要条件,提出一类广义变分不等式问题的神经网络模型.通过构造Lyapunov函数,在适当的条件下证明了新模型是Lyapunov稳定的,并且全局收敛和指数收敛于原问题的解.数值试验表明,该神经网络模型是有效的和可行的.
Based on the necessary and sufficient conditions of the solution,this paper proposed a neural network model for a class of generalized variational inequality problem.Under proper conditions,the new model is proved to be Lyapunov stable and convergent to a solution of the original problem by introducing the Lyapunov functions and globally exponential stability of the neural network model for generalized variational inequality problem is studied.The efficiency and feasibility of the proposed model is confirmed by numerical experiments.
Based on the necessary and sufficient conditions of the solution,this paper proposed a neural network model for a class of generalized variational inequality problem.Under proper conditions,the new model is proved to be Lyapunov stable and convergent to a solution of the original problem by introducing the Lyapunov functions and globally exponential stability of the neural network model for generalized variational inequality problem is studied.The efficiency and feasibility of the proposed model is confirmed by numerical experiments.
引文
[1]Noor M A.Merit functions for general variational inequalities[J].J Math Anal Appl,2006,316:736-752.
[2]董宁,莫沿艺,高兴宝.解广义变分不等式的神经网络[J].工程数学学报,2004,8(21):78-82.
[3]Hartman P,Stampacchia G.On some nonlinear elliptic differential functional equations[J].Acta Math,1966,115(1):271-310.
[4]胡艳红,宋文.广义变分不等式的广义间隙函数和误差界[J].应用数学和力学,2009,30(3):301-308.
[5]谭露琳.空间中变分不等式问题的存在性与例外簇[J].华南师范大学学报:自然科学版,2009,3:22-24.
[6]韦丽兰,黄力人.赋范空间中强变分不等式问题的α-例外簇[J].华南师范大学学报:自然科学版,2011,1:43-45.
[7]侯增广,吴沧浦.数学规划的求解与广义Hopfield神经网络[J].运筹学学报,1997,1(2):48-56.
[8]李有梅,申建中,徐宗本.投影型神经网络算法的全局收敛性分析[J].计算机学报,2005,28(7):1178-1184.
[9]Gao X B.A novel neural network for nonlinear convex programming[J].IEEE Trans on Neural Networks,2004,15(3):613-621.
[10]Lan H Y,Cui Y S.A neural network method for solving a system of linear variational inequalities[J].Chaos,Solitons and Fractals,2009,41:1245-1252.
[11]Ding K,Huang N J.A new class of interval projection neural networks for solving interval quadratic program[J].Chaos,Solitons and Fractals,2008,35:718-725.
[12]Xia Y S,Feng G.A new neural network for solving nonlinear projection equations[J].Neural Networks,2007,20:577-589.
[13]段广仁.线性系统理论[M].哈尔滨工业大学出版社,2004.
[2]董宁,莫沿艺,高兴宝.解广义变分不等式的神经网络[J].工程数学学报,2004,8(21):78-82.
[3]Hartman P,Stampacchia G.On some nonlinear elliptic differential functional equations[J].Acta Math,1966,115(1):271-310.
[4]胡艳红,宋文.广义变分不等式的广义间隙函数和误差界[J].应用数学和力学,2009,30(3):301-308.
[5]谭露琳.空间中变分不等式问题的存在性与例外簇[J].华南师范大学学报:自然科学版,2009,3:22-24.
[6]韦丽兰,黄力人.赋范空间中强变分不等式问题的α-例外簇[J].华南师范大学学报:自然科学版,2011,1:43-45.
[7]侯增广,吴沧浦.数学规划的求解与广义Hopfield神经网络[J].运筹学学报,1997,1(2):48-56.
[8]李有梅,申建中,徐宗本.投影型神经网络算法的全局收敛性分析[J].计算机学报,2005,28(7):1178-1184.
[9]Gao X B.A novel neural network for nonlinear convex programming[J].IEEE Trans on Neural Networks,2004,15(3):613-621.
[10]Lan H Y,Cui Y S.A neural network method for solving a system of linear variational inequalities[J].Chaos,Solitons and Fractals,2009,41:1245-1252.
[11]Ding K,Huang N J.A new class of interval projection neural networks for solving interval quadratic program[J].Chaos,Solitons and Fractals,2008,35:718-725.
[12]Xia Y S,Feng G.A new neural network for solving nonlinear projection equations[J].Neural Networks,2007,20:577-589.
[13]段广仁.线性系统理论[M].哈尔滨工业大学出版社,2004.