Smoothing techniques and difference of convex functions algorithms for image reconstructions. (2nd August 2020)

• Record Type: Journal Article
• Authors: Mau Nam, Nguyen; Hoai An, Le Thi; Giles, Daniel; Thai An, Nguyen
• Is Part Of: Optimization. Volume 69:Number 7/8(2020)
• Page Start: 1601
• Page End: 1633
• Publication Date: 2020-08-02
• Subjects: Generalized differentiation -- Nesterov's smoothing techniques -- DC algorithm -- image reconstruction; 49J52 -- 49J53 -- 90C31; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1648467
• Languages: English
• ISSNs: 0233-1934

Abstract

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.