A general double-proximal gradient algorithm for d.c. programming

A general double-proximal gradient algorithm for d.c. programming

The possibilities of exploiting the special structure of d.c. programs, which consist of optimizing the difference of convex functions, are currently more or less limited to variants of the DCA proposed by Pham Dinh Tao and Le Thi Hoai An in 1997. These assume that either the convex or the concave part, or both, are evaluated by one of their subgradients. In this paper we propose an algorithm w...

The proximal-proximal gradient algorithm

We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a composition of a proper closed convex function P and a nonzero affine map, with the proximal mappings of τP , τ > 0, easy to compute. In this case, a direct applic...

Accelerated Proximal Gradient Methods for Nonconvex Programming

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...

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 ...