The goal of the sparse approximation problem is to approximate a target signal using a
linear combination of a few elementary signals drawn from a fixed collection. This paper …

We study minimization of the difference of \ell_1 and \ell_2 norms as a nonconvex and
Lipschitz continuous metric for solving constrained and unconstrained compressed sensing …

Accurate signal recovery or image reconstruction from indirect and possibly undersampled
data is a topic of considerable interest; for example, the literature in the recent field of …

The linearly constrained matrix rank minimization problem is widely applicable in many
fields such as control, signal processing and system identification. The tightest convex …

One of the major issues in stochastic gradient descent (SGD) methods is how to choose an
appropriate step size while running the algorithm. Since the traditional line search technique …

We generalize Newton-type methods for minimizing smooth functions to handle a sum of two
convex functions: a smooth function and a nonsmooth function with a simple proximal …

This paper develops a general framework for solving a variety of convex cone problems that
frequently arise in signal processing, machine learning, statistics, and other fields. The …

We develop a fast and robust algorithm for solving large-scale convex composite
optimization models with an emphasis on the \ell_1-regularized least squares regression …

We propose Shotgun, a parallel coordinate descent algorithm for minimizing L1-regularized
losses. Though coordinate descent seems inherently sequential, we prove convergence …

The forward–backward splitting method (FBS) for minimizing a nonsmooth composite
function can be interpreted as a (variable-metric) gradient method over a continuously …