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Home / Optimization, Volume 69, Numbers 7-8

Smoothing techniques and difference of convex functions algorithms for image reconstructions

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Authors: Mau Nam, Nguyen 1 ; Hoai An, Le Thi 2 ; Giles, Daniel 3 ; Thai An, Nguyen 4 ; 

Source: Optimization, Volume 69, Numbers 7-8, 2 August 2020, pp. 1601-1633(33)

Publisher: Taylor and Francis Ltd

DOI: https://doi.org/10.1080/02331934.2019.1648467

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 [Inline formula] regularization.

Keywords: 49J52; 49J53; 90C31; DC algorithm; Generalized differentiation; Nesterov's smoothing techniques; image reconstruction

Document Type: Research Article

Affiliations: 1: Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR, USA 2: Computer Science and Applications Department, LGIPM, University of Lorraine, Metz, France 3: Department of Mathematics, Santa Barbara City College, Santa Barbara, CA, USA 4: Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China

Publication date: 02 August 2020

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