Discerning the linear convergence of ADMM for structured convex optimization through the lens of variational analysis

Despite the rich literature, the linear convergence of alternating direction method of multipliers (ADMM) has not been fully understood even for the convex case. For example, the linear convergence of ADMM can be empirically observed in a wide range of applications, while existing theoretical results seem to be too stringent to be satisfied or too … Read more

Block Coordinate Proximal Gradient Method for Nonconvex Optimization Problems: Convergence Analysis

We propose a block coordinate proximal gradient method for a composite minimization problem with two nonconvex function components in the objective while only one of them is assumed to be differentiable. Under some per-block Lipschitz-like conditions based on Bregman distance, but without the global Lipschitz continuity of the gradient of the differentiable function, we prove … Read more