Neural network for constrained nonsmooth optimization using Tikhonov regularization
Neural network for constrained nonsmooth optimization using Tikhonov regularization
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DOI：
10.1016/j.neunet.2014.12.007
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发表时间：
2015-03
期刊：
影响因子：
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通讯作者：
Sitian Qin;Dejun Fan;Guangxi Wu;Lijun Zhao
中科院分区：
文献类型：
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作者：
Sitian Qin;Dejun Fan;Guangxi Wu;Lijun Zhao
提出了一种基于Tikhonov正则化方法的单层神经网络来求解非光滑凸优化问题。首先证明了原问题的最优解可以用一个强凸优化问题的最优解来逼近。然后证明了对于任意初始点，所提出的神经网络的状态在有限时间内进入等式可行域，并且全局收敛于相关强凸优化问题的唯一最优解.与现有的神经网络相比，该神经网络具有较低的模型复杂度，并且不需要惩罚参数。最后给出了一些数值例子和应用，以说明所提出的神经网络的有效性和改进。
This paper presents a one-layer neural network to solve nonsmooth convex optimization problems based on the Tikhonov regularization method. Firstly, it is shown that the optimal solution of the original problem can be approximated by the optimal solution of a strongly convex optimization problems. Then, it is proved that for any initial point, the state of the proposed neural network enters the equality feasible region in finite time, and is globally convergent to the unique optimal solution of the related strongly convex optimization problems. Compared with the existing neural networks, the proposed neural network has lower model complexity and does not need penalty parameters. In the end, some numerical examples and application are given to illustrate the effectiveness and improvement of the proposed neural network.