Backtracking Strategies for Accelerated Descent Methods with Smooth Composite Objectives
针对强凸复合目标函数，提出一种允许步长局部增减的回溯策略，证明加速收敛速率并给出数值结果。
We present and analyze a backtracking strategy for a general fast iterative shrinkage/thresholding algorithm proposed by Chambolle and Pock [Acta Numer., 25 (2016), pp. 161--319] for strongly convex composite objective functions. Unlike classical Armijo-type line searching, our backtracking rule allows for local increasing and decreasing of the descent step size (i.e., proximal parameter) along the iterations. We prove accelerated convergence rates and show numerical results for some exemplar problems.