Smoothing techniques and difference of convex functions algorithms for image reconstructions. (2nd August 2020) - Mau Nam, Nguyen; Hoai An, Le Thi; Giles, Daniel; Thai An, Nguyen
Abstract: In this paper, we study characterizations of differentiability for real-valued functions based on generalized differentiation. These characterizations provide the mathematical foundation for Nesterov's smoothing techniques in infinite dimensions. As an application, we provide a simple approach to image reconstructions based on Nesterov's smoothing and algorithms for minimizing differences of convex (DC) functions that involve the ℓ 1 − ℓ 2 regularization.