一类二次规划问题的比例时滞神经网络的渐近稳定性  

Asymptotic stability of projection neural networks with proportional delays for a class of quadratic programming problem

作　　者：孙颖倩 周立群[1] 王宇[1] 张诗茹 张渝佶 SUN Yingqian;ZHOU Liqun;WANG Yu;ZHANG Shiru;ZHANG Yuji(College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2022年第4期11-16,22,共7页Journal of Tianjin Normal University：Natural Science Edition

基　　金：天津市自然科学基金资助项目(18JCYBJC85800);天津市普通高等学校本科教学质量与教学改革研究计划资助项目(B201006505);国家级大学生创新训练计划资助项目(202110065004)。

摘　　要：利用比例时滞投影神经网络求解一类二次规划问题,根据鞍点定理讨论二次规划问题解的存在性.通过Lagrange函数法和投影定理,将二次规划问题转化为比例时滞投影神经网络,并说明平衡点即为二次规划问题的最优解.通过构造Lyapunov泛函,利用内积的性质,得到保证该网络平衡点全局渐近稳定的判定准则.最后,利用2个数值算例及仿真检验判定准则的有效性.A class of quadratic programming problem by projection neural networks with proportional delays is investigated.According to the saddle point theorem,the existence of the solution to the quadratic programming problem is discussed.Through the Lagrange function method and the projection theorem,the quadratic programming problem is transformed into a projection neural network with proportional delays,which shows that the equilibrium point is the optimal solution to the quadratic programming problem. By constructing the Lyapunov functional and using the property of the inner product,the criterion for the global asymptotic stability of the equilibrium point of the network is obtained. Finally,two numerical examples and simulations are used to test the validity of the obtained criterion.

关 键 词：二次规划问题 比例时滞 LYAPUNOV泛函 全局渐近稳定性 投影神经网络 

分 类 号：O175.13[理学—数学]