Smoothing Techniques and Difference of Convex Functions Algorithms for Image Reconstructions
Research of Nguyen Mau Nam was partly supported by the National Science Foundation (Division of Mathematical Sciences) under grant DMS-1716057. Research of Nguyen Thai An was supported by the China Postdoctoral Science Foundation under grant No. 2017M622991.
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 ℓ1−ℓ2 regularization.
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Mau Nam, N., Hoai An, L. T., Giles, D., & Thai An, N. (2019). Smoothing techniques and difference of convex functions algorithms for image reconstructions. Optimization, 1-33.