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Characterizations of Differentiability, Smoothing Techniques and DC Programming with Applications to Image Reconstructions

Nguyen Mau Nam (mnn3***at***pdx.edu)
Daniel Giles (djgiles1***at***pipeline.sbcc.edu)
Le Thi Hoai An (hoai-an.le-thi***at***univ-lorraine.fr)
Nguyen Thai An (thaian2784***at***gmail.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


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Entry Submitted: 07/18/2018
Entry Accepted: 07/18/2018
Entry Last Modified: 08/24/2018

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