An accelerated dual proximal gradient method for applications in viscoplasticity

An Accelerated Proximal Coordinate Gradient Method

We develop an accelerated randomized proximal coordinate gradient (APCG) method, for solving a broad class of composite convex optimization problems. In particular, our method achieves faster linear convergence rates for minimizing strongly convex functions than existing randomized proximal coordinate gradient methods. We show how to apply the APCG method to solve the dual of the regularized em...

Accelerated Proximal Gradient Methods for Nonconvex Programming

Nonconvex and nonsmooth problems have recently received considerable attention in signal/image processing, statistics and machine learning. However, solving the nonconvex and nonsmooth optimization problems remains a big challenge. Accelerated proximal gradient (APG) is an excellent method for convex programming. However, it is still unknown whether the usual APG can ensure the convergence to a...

Accelerated Proximal Gradient Methods for Nonconvex Programming

An Adaptive Accelerated Proximal Gradient Method and its Homotopy Continuation for Sparse Optimization

We first propose an adaptive accelerated proximal gradient (APG) method for minimizing strongly convex composite functions with unknown convexity parameters. This method incorporates a restarting scheme to automatically estimate the strong convexity parameter and achieves a nearly optimal iteration complexity. Then we consider the l1regularized least-squares (l1-LS) problem in the high-dimensio...

An Adaptive Accelerated Proximal Gradient Method and its Homotopy Continuation for Sparse Optimization

We consider optimization problems with an objective function that is the sum of two convex terms: one is smooth and given by a black-box oracle, and the other is general but with a simple, known structure. We first present an accelerated proximal gradient (APG) method for problems where the smooth part of the objective function is also strongly convex. This method incorporates an efficient line...