We present a condition on the matrix of an underdetermined linear system which guarantees
that the solution of the system with minimal ℓ q -quasinorm is also the sparsest one. This …

In this paper, we first study $\ell_q$ minimization and its associated iterative reweighted
algorithm for recovering sparse vectors. Unlike most existing work, we focus on unconstrained $\…

Spline functions are universally recognized as highly effective tools in approximation theory,
computer-aided geometric design, image analysis, and numerical analysis. The theory of …

This paper introduces a parallel and distributed algorithm for solving the following
minimization problem with linear constraints: $$\begin{aligned} \text {minimize} ~~&f_1(\mathbf{x}_1) …

We study an unconstrained version of the $\ell_q$ minimization for the sparse solution of
underdetermined linear systems for $0<q\leq1$. Although the minimization is nonconvex when …

We study the initial boundary value problem of two-dimensional viscous Boussinesq
equations over a bounded domain with smooth boundary. We show that the equations have a …

This paper studies the long-existing idea of adding a nice smooth function to “smooth” a
nondifferentiable objective function in the context of sparse optimization, in particular, the …

In this paper, the asymptotic behavior of penalized spline estimators is studied using bivariate
splines over triangulations and an energy functional as the penalty. A convergence rate for …

Two simple constructive methods are presented to compute compactly supported tight
wavelet frames for any given refinable function whose mask satisfies the QMF or sub-QMF …

In this paper, we propose an efficient and scalable low rank matrix completion algorithm.
The key idea is to extend the orthogonal matching pursuit method from the vector case to the …