A Generalized Hopfield Network for Nonsmooth Constrained Convex Optimization: Lie Derivative Approach

Li Chaojie; Yu Xinghuo; Huang Tingwen; Chen Guo; He Xing

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A Generalized Hopfield Network for Nonsmooth Constrained Convex Optimization: Lie Derivative Approach

机译：非光滑约束凸优化的广义Hopfield网络：Lie导数方法

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This paper proposes a generalized Hopfield network for solving general constrained convex optimization problems. First, the existence and the uniqueness of solutions to the generalized Hopfield network in the Filippov sense are proved. Then, the Lie derivative is introduced to analyze the stability of the network using a differential inclusion. The optimality of the solution to the nonsmooth constrained optimization problems is shown to be guaranteed by the enhanced Fritz John conditions. The convergence rate of the generalized Hopfield network can be estimated by the second-order derivative of the energy function. The effectiveness of the proposed network is evaluated on several typical nonsmooth optimization problems and used to solve the hierarchical and distributed model predictive control four-tank benchmark.

机译：本文提出了一种广义Hopfield网络来解决一般约束凸优化问题。首先，证明了Filippov广义Hopfield网络解的存在性和唯一性。然后，引入Lie导数以使用微分包含来分析网络的稳定性。非光滑约束优化问题的解决方案的最优性通过增强的Fritz John条件得以保证。广义Hopfield网络的收敛速度可以通过能量函数的二阶导数来估计。在几个典型的非平稳优化问题上评估了所提出网络的有效性，并用于解决分层和分布式模型预测控制四箱基准。

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来源
《Neural Networks and Learning Systems, IEEE Transactions on》 |2016年第2期|308-321|共14页
作者
Li Chaojie; Yu Xinghuo; Huang Tingwen; Chen Guo; He Xing;
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作者单位

School of Electrical and Computer Engineering, RMIT University, Melbourne, Australia;

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正文语种 eng
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关键词
Constraints; Filippov solutions; Hopfield network; Lie derivative; Lie derivative.; enhanced Fritz John conditions; global optimization;

机译：约束;Filippov解;Hopfield网络;Lie导数;Lie导数;改进的Fritz John条件;全局优化;

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A Generalized Hopfield Network for Nonsmooth Constrained Convex Optimization: Lie Derivative Approach

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