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Deep structures consisting of many layers of nonlinearities have a high potential of expressing complex relations if properly initialized. Autoencoders play a complementary role in training a deep structure by initializing each layer in a greedy unsupervised manner. Due to the high capacity presented by autoencoders, these structures need to be regularized. While mathematical regularizers (based on weight decay, sparsity, etc.) and structural ones (by way of, e.g., denoising and dropout) have been well studied in the literature, quite a few papers have addressed the problem of training autoencoder with non-smooth regularization. In this paper, we address the problem of training autoencoder...