Backtracking strategies for accelerated descent methods with smooth\n composite objectives

2017/09/26 by Luca Calatroni, Calatroni, Luca, Antonin Chambolle +1 · 2 citations
Computer Science · Engineering · Mathematics · Medicine · #65F22 #90C25 #FOS: Mathematics #Medical Image Segmentation Techniques #Medical Imaging Techniques and Applications #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1709.09004

openalex publication_date 2017/09/26 · openalex created_date 2022/11/21 · openalex updated_date 2026/07/28

Abstract

We present and analyse a backtracking strategy for a general Fast Iterative\nShrinkage/Thresholding Algorithm which has been recently proposed in\n(Chambolle, Pock, 2016) for strongly convex objective functions. Differently\nfrom classical Armijo-type line searching, our backtracking rule allows for\nlocal increasing and decreasing of the descent step size (i.e. proximal\nparameter) along the iterations. For such strategy accelerated convergence\nrates are proved and numerical results are shown for some exemplar imaging\nproblems.\n

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