Two-level optimization approach with accelerated proximal gradient for objective measures in sparse speech reconstruction

Proximal gradient algorithm for group sparse optimization

In this paper, we propose a proximal gradient algorithm for solving a general nonconvex and nonsmooth optimization model of minimizing the summation of a C1,1 function and a grouped separable lsc function. This model includes the group sparse optimization via lp,q regularization as a special case. Our algorithmic scheme presents a unified framework for several well-known iterative thresholding ...

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...

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