Solving Composite Optimization Problems and Applications in Image Processing and Data Analysis

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Eftekhari, Asieh | 2021

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 53865 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi-Amiri, Nezamoddin
Abstract:
At first, we introduce composite optimization problems some review the proposed methods to solve these problems. To solve the composite optimization problems with strongly convex objective function, recently Chamboll and Pock proposed a general fast iterative shrinkage and thresholding algorithm (GFISTA). After that, Calatroni and Chambolle proposed a backtracking strategy for this algorithm. Unlike classical Armijo-type line searching, proposed backtracking rule allows for local increasing or decreasing of the descent step size along the iterations. In this thesis, we describe this algorithm with backtracking and prove its accelerated convergence rate. We also discuss some heuristic restarting strategies in the case when the strong convexity parameters are unknown. Finally, we implement and test the introduced algorithms on some problems that can be used in image processing or data analysis in MATLAB software environment. The obtained results show that GFISTA with backtracking strategy proposed by Calatroni and Chambolle has a better convergence rate than the ones due to other algorithms
Keywords:
Image Denoising ; Acceleration ; Image Processing ; Data Analysis ; Forward-Backward Splitting ; Elastic Net ; Composite Optimization