- Characterizations of Differentiability, Smoothing Techniques and DC Programming with Applications to Image Reconstructions Nguyen Mau Nam (mnn3pdx.edu) Daniel Giles (djgiles1pipeline.sbcc.edu) Le Thi Hoai An (hoai-an.le-thiuniv-lorraine.fr) Nguyen Thai An (thaian2784gmail.com) 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 techniques and DC programming that involves the $\ell_1-\ell_2$ regularization. Keywords: DC programming; the DCA; Fenchel conjugate; inpainting; dictionary learning Category 1: Convex and Nonsmooth Optimization Citation: Download: [PDF]Entry Submitted: 07/18/2018Entry Accepted: 07/18/2018Entry Last Modified: 08/24/2018Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.