A general projection neural network for solving monotone variational inequalities and related optimization problems
A general projection neural network for solving monotone variational inequalities and related optimization problems
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DOI：
10.1109/tnn.2004.824252
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发表时间：
2004-03
影响因子：
--
通讯作者：
Youshen Xia;Jun Wang
中科院分区：
文献类型：
--
作者：
Youshen Xia;Jun Wang
近年来，一种求解单调变分不等式和约束优化问题的投影神经网络被提出。在本文中，我们提出了一个通用的投影神经网络解决更广泛的一类变分不等式和相关的优化问题。除了其简单的结构和低复杂度，所提出的神经网络包括现有的神经网络优化，如投影神经网络，原始-对偶神经网络，和对偶神经网络，作为特殊情况。在适当的条件下，证明了广义投影神经网络的全局收敛性、全局渐近稳定性和全局指数稳定性。在较弱的条件下，对一般投影神经网络的两种特殊情况，得到了几个改进的稳定性判据。仿真结果验证了所提出的神经网络的有效性和特点。
Recently, a projection neural network for solving monotone variational inequalities and constrained optimization problems was developed. In this paper, we propose a general projection neural network for solving a wider class of variational inequalities and related optimization problems. In addition to its simple structure and low complexity, the proposed neural network includes existing neural networks for optimization, such as the projection neural network, the primal-dual neural network, and the dual neural network, as special cases. Under various mild conditions, the proposed general projection neural network is shown to be globally convergent, globally asymptotically stable, and globally exponentially stable. Furthermore, several improved stability criteria on two special cases of the general projection neural network are obtained under weaker conditions. Simulation results demonstrate the effectiveness and characteristics of the proposed neural network.