神经网络求解一类稀疏优化问题  

Neural network for solving a class of optimization problems in sparsity

作　　者：魏喆[1] 李庆发 边伟 WEI Zhe;LI Qing-fa;BIAN Wei(Department of Mathematics,Heilongjiang Institute of Technology,Harbin 150050,China;Department of Mathematics,Harbin Institute of Technology,Harbin,1500001)

机构地区：[1]黑龙江工程学院数学系,哈尔滨150050 [2]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《哈尔滨商业大学学报（自然科学版）》2018年第6期741-744,756,共5页Journal of Harbin University of Commerce：Natural Sciences Edition

摘　　要：利用近年来应用比较广泛的神经网络算法求解了一类在信号还原中具有广泛应用的非Lipschitz约束优化问题.以非光滑分析与最优化理论为基础,发展和推广非Lipschitz稀疏优化问题的基础理论研究及其与图像还原问题的联系,利用光滑化技术以及投影方法构造了一类优化问题的神经网络,由此证明了所构造的神经网络的解是全局存在且一致有界的.还给出了优化模型的稳定点的定义,并证明了所构造的神经网络解轨线的聚点均为稳定点.利用Matlab软件,进行了数值模拟,并验证了所提出的神经网络算法的性能.In this paper, the neural network algorithm was used to solve a class of non - Lips-chitz constrained optimization problems which were widely used in signal reduction. The neu-ral network of optimization problem was constructed by smoothing technique and projection.It was proved that the solution of the constructed neural network was globally existent and u-niformy bounded. In addition, the stationary points of the optimization model are defined. Itwas proved that the accumulation points of the constructed neural network were the stationary points. Finally, the pefformance of the algorithm was verified by numerical simulation.

关 键 词：非Lipschitz 约束优化 神经网络 稳定点 广义梯度 光滑函数 

分 类 号：O436[机械工程—光学工程]