Linearly Constrained Nonsmooth Optimization for Training Autoencoders
提出一种带L1范数惩罚的线性约束正则化模型用于训练自编码器，并设计平滑近端梯度算法求解，数值实验验证了算法的效率和鲁棒性。
A regularized minimization model with $l_1$-norm penalty (RP) is introduced for training the autoencoders that belong to a class of two-layer neural networks. We show that the RP can act as an exact penalty model which shares the same global minimizers, local minimizers, and d(irectional)-stationary points with the original regularized model under mild conditions. We construct a bounded box region that contains at least one global minimizer of the RP, and propose a linearly constrained regularized minimization model with $l_1$-norm penalty (LRP) for training autoencoders. A smoothing proximal gradient algorithm is designed to solve the LRP. Convergence of the algorithm to a generalized d-stationary point of the RP and LRP is delivered. Comprehensive numerical experiments convincingly illustrate the efficiency as well as the robustness of the proposed algorithm.