Related papers: Group sparse optimization via $\ell_{p,q}$ regular…

We establish an equivalence between the $\ell_2$-regularized solution path for a convex loss function, and the solution of an ordinary differentiable equation (ODE). Importantly, this equivalence reveals that the solution path can be viewed…

In this paper we look at a particular problem related to under-determined linear systems of equations with sparse solutions. $\ell_1$-minimization is a fairly successful polynomial technique that can in certain statistical scenarios find…

We propose a convex variational principle to find sparse representation of low-lying eigenspace of symmetric matrices. In the context of electronic structure calculation, this corresponds to a sparse density matrix minimization algorithm…

In this paper, we study the problem of recovering a group sparse vector from a small number of linear measurements. In the past the common approach has been to use various "group sparsity-inducing" norms such as the Group LASSO norm for…

We study a hybrid conditional gradient - smoothing algorithm (HCGS) for solving composite convex optimization problems which contain several terms over a bounded set. Examples of these include regularization problems with several norms as…

We consider the problem of minimizing a high-dimensional objective function, which may include a regularization term, using (possibly noisy) evaluations of the function. Such optimization is also called derivative-free, zeroth-order, or…

In this paper we present an active-set method for the solution of $\ell_1$-regularized convex quadratic optimization problems. It is derived by combining a proximal method of multipliers (PMM) strategy with a standard semismooth Newton…

Parameter estimation from multiple measurement vectors (MMVs) is a fundamental problem in many signal processing applications, e.g., spectral analysis and direction-of- arrival estimation. Recently, this problem has been address using prior…

Stochastic optimization lies at the core of most statistical learning models. The recent great development of stochastic algorithmic tools focused significantly onto proximal gradient iterations, in order to find an efficient approach for…

The prevalence of neural networks in society is expanding at an increasing rate. It is becoming clear that providing robust guarantees on systems that use neural networks is very important, especially in safety-critical applications. A…

Popular machine learning estimators involve regularization parameters that can be challenging to tune, and standard strategies rely on grid search for this task. In this paper, we revisit the techniques of approximating the regularization…

We propose in this contribution a method for l one regularization in prototype based relevance learning vector quantization (LVQ) for sparse relevance profiles. Sparse relevance profiles in hyperspectral data analysis fade down those…

This work addresses the recovery and demixing problem of signals that are sparse in some general dictionary. Involved applications include source separation, image inpainting, super-resolution, and restoration of signals corrupted by…

Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…

This paper is concerned with a class of zero-norm regularized piecewise linear-quadratic (PLQ) composite minimization problems, which covers the zero-norm regularized $\ell_1$-loss minimization problem as a special case. For this class of…

Sparse logistic regression, as an effective tool of classification, has been developed tremendously in recent two decades, from its origination the $\ell_1$-regularized version to the sparsity constrained models. This paper is carried out…

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

We are concerned with a class of nonconvex and nonsmooth composite optimization problems, comprising a twice differentiable function and a prox-regular function. We establish a sufficient condition for the proximal mapping of a prox-regular…

We present a framework for smooth optimization of explicitly regularized objectives for (structured) sparsity. These non-smooth and possibly non-convex problems typically rely on solvers tailored to specific models and regularizers. In…

Compressed Sensing using $\ell_1$ regularization is among the most powerful and popular sparsification technique in many applications, but why has it not been used to obtain sparse deep learning model such as convolutional neural network…