An Improved Dual Neural Network for Solving a Class of Quadratic Programming Problems and Its $k$-Winners-Take-All Application
An Improved Dual Neural Network for Solving a Class of Quadratic Programming Problems and Its $k$-Winners-Take-All Application
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DOI：
10.1109/tnn.2008.2003287
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发表时间：
2008-12
影响因子：
--
通讯作者：
Xiaolin Hu;Jun Wang
中科院分区：
文献类型：
--
作者：
Xiaolin Hu;Jun Wang
提出了一种新的递归神经网络用于求解一类凸二次规划（QP）问题，其中目标函数中的二次项是变量的欧几里德范数的平方.这种特殊的结构导致了一组简单的最优性条件的问题，神经网络模型的制定。与现有的一般凸二次规划神经网络相比，新模型结构简单，易于实现。新模型可以看作是文献中对偶神经网络的改进版本。基于新的模型，一个简单的神经网络能够解决$k$-赢家通吃（$k$-WTA）的问题。该神经网络的稳定性和全局收敛性得到了严格的证明和仿真结果的证实。
This paper presents a novel recurrent neural network for solving a class of convex quadratic programming (QP) problems, in which the quadratic term in the objective function is the square of the Euclidean norm of the variable. This special structure leads to a set of simple optimality conditions for the problem, based on which the neural network model is formulated. Compared with existing neural networks for general convex QP, the new model is simpler in structure and easier to implement. The new model can be regarded as an improved version of the dual neural network in the literature. Based on the new model, a simple neural network capable of solving the $k$-winners-take-all ( $k$-WTA) problem is formulated. The stability and global convergence of the proposed neural network is proved rigorously and substantiated by simulation results.