A New Recurrent Neural Network for Solving Convex Quadratic Programming Problems With an Application to the $k$-Winners-Take-All Problem
A New Recurrent Neural Network for Solving Convex Quadratic Programming Problems With an Application to the $k$-Winners-Take-All Problem
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DOI：
10.1109/tnn.2008.2011266
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发表时间：
2009-04
影响因子：
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通讯作者：
Xiaolin Hu;Bo Zhang-
中科院分区：
文献类型：
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作者：
Xiaolin Hu;Bo Zhang-
提出了一种新的递归神经网络用于求解凸二次规划问题。与已有的神经网络相比，该网络具有弱条件下的全局收敛性，结构复杂度低，不需要矩阵求逆等特点。它是神经网络家族中解决线性或二次规划问题的一种有竞争力的选择。另外，通过变量替换，发现该网络是一个求解极大极小问题的已有模型。在这个意义上，它也可以被看作是极大极小神经网络的一个特例。在此基础上，设计了一个复杂度为O（n）的k-WTA网络，该网络结构简单，具有全局收敛性，并能处理某些病态情况.数值模拟验证了理论结果。更重要的是，本文提出的网络设计方法具有很大的潜力，可以激励其他沿着同一路线的竞争性发明。
In this paper, a new recurrent neural network is proposed for solving convex quadratic programming (QP) problems. Compared with existing neural networks, the proposed one features global convergence property under weak conditions, low structural complexity, and no calculation of matrix inverse. It serves as a competitive alternative in the neural network family for solving linear or quadratic programming problems. In addition, it is found that by some variable substitution, the proposed network turns out to be an existing model for solving minimax problems. In this sense, it can be also viewed as a special case of the minimax neural network. Based on this scheme, a k-winners-take-all (k-WTA) network with O(n) complexity is designed, which is characterized by simple structure, global convergence, and capability to deal with some ill cases. Numerical simulations are provided to validate the theoretical results obtained. More importantly, the network design method proposed in this paper has great potential to inspire other competitive inventions along the same line.