求解二次规划问题的离散时间神经网络的收敛性分析

路洋,李德伟,席裕庚,卢建波

系统科学与数学 ›› 2012, Vol. 32 ›› Issue (11) : 1343-1353.

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PDF(639 KB)
系统科学与数学 ›› 2012, Vol. 32 ›› Issue (11) : 1343-1353. DOI: 10.12341/jssms11991
论文

求解二次规划问题的离散时间神经网络的收敛性分析

    路洋,李德伟,席裕庚,卢建波
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CONVERGENCE ANALYSIS OF DISCRETE-TIME NEURAL NETWORK FOR SOLVING QUADRATIC PROGRAMMING PROBLEMS

    LU Yang ,LI Dewei ,XI Yugeng ,LU Jianbo
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摘要

对求解二次规划问题的离散时间神经网络的收敛性进行了分析, 通过选取适当的李雅普诺夫函数给出了网络全局收敛的充分条件,  并在该条件下研究了网络的收敛速度,  分别对问题的不等式约束左矩阵行满秩和非行满秩的情况进行了讨论,  得到了在上述充分条件下对于不等式约束左矩阵行满秩和非行满秩的问题均有网络指数收敛的结论,  通过仿真验证了结论的正确性.

Abstract

The convergence property of discrete-time neural network for quadratic programming is analyzed. By choosing a proper Lyapunov function, a sufficient  ondition for global convergence is obtained. The convergence rate under the condition is also investigated through a in-depth discussion about full-row-rank inequality constraint left matrix condition nd non-full-row-rank inequality constraint left matrix condition, respectively, and the exponential convergence property for both full-row rank and non-full-row rank inequality constraint left matrix conditions under the mentioned sufficient condition is proved. Simulation result
verifies the validity of the theoretical results obtained in this paper.

关键词

二次规划 / 神经网络 / 离散时间 / 收敛性

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路洋,李德伟,席裕庚,卢建波. 求解二次规划问题的离散时间神经网络的收敛性分析. 系统科学与数学, 2012, 32(11): 1343-1353. https://doi.org/10.12341/jssms11991
LU Yang ,LI Dewei ,XI Yugeng ,LU Jianbo. CONVERGENCE ANALYSIS OF DISCRETE-TIME NEURAL NETWORK FOR SOLVING QUADRATIC PROGRAMMING PROBLEMS. Journal of Systems Science and Mathematical Sciences, 2012, 32(11): 1343-1353 https://doi.org/10.12341/jssms11991
中图分类号: 90C20    92B20    65M12   
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