Related papers: Sparse Convex Optimization via Adaptively Regulari…

We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…

In recent studies on sparse modeling, the nonconvex regularization approaches (particularly, $L_{q}$ regularization with $q\in(0,1)$) have been demonstrated to possess capability of gaining much benefit in sparsity-inducing and efficiency.…

The convergence of the generalized alternating projection (GAP) algorithm is studied in this paper to solve the compressive sensing problem $\yv = \Amat \xv + \epsilonv$. By assuming that $\Amat\Amat\ts$ is invertible, we prove that GAP…

Online Convex Optimization plays a key role in large scale machine learning. Early approaches to this problem were conservative, in which the main focus was protection against the worst case scenario. But recently several algorithms have…

We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…

Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper…

This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…

In numerous substitution models for the $\l_{0}$-norm minimization problem $(P_{0})$, the $\l_{p}$-norm minimization $(P_{p})$ with $0<p<1$ have been considered as the most natural choice. However, the non-convex optimization problem…

This paper presents a novel hybrid algorithm for minimizing the sum of a continuously differentiable loss function and a nonsmooth, possibly nonconvex, sparse regularization function. The proposed method alternates between solving a…

Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…

We propose greedy and local search algorithms for rank-constrained convex optimization, namely solving $\underset{\mathrm{rank}(A)\leq r^*}{\min}\, R(A)$ given a convex function $R:\mathbb{R}^{m\times n}\rightarrow \mathbb{R}$ and a…

An accelerated class of adaptive scheme of iterative thresholding algorithms is studied analytically and empirically. They are based on the feedback mechanism of the null space tuning techniques (NST+HT+FB). The main contribution of this…

Sparse signals can be possibly reconstructed by an algorithm which merges a traditional nonlinear optimization method and a certain thresholding technique. Different from existing thresholding methods, a novel thresholding technique…

In many statistical learning problems, it is desired that the optimal solution conforms to an a priori known sparsity structure represented by a directed acyclic graph. Inducing such structures by means of convex regularizers requires…

Motivated by the question of optimal functional approximation via compressed sensing, we propose generalizations of the Iterative Hard Thresholding and the Compressive Sampling Matching Pursuit algorithms able to promote sparse in levels…

In this paper we revisit the well-known constrained projection approximation subspace tracking algorithm (CPAST) and derive, for the first time, non-asymptotic error bounds. Furthermore, we introduce a novel sparse modification of CPAST…

We consider the problem of minimizing an objective function that is the sum of a convex function and a group sparsity-inducing regularizer. Problems that integrate such regularizers arise in modern machine learning applications, often for…

This article proposes novel sparsity-aware space-time adaptive processing (SA-STAP) algorithms with $l_1$-norm regularization for airborne phased-array radar applications. The proposed SA-STAP algorithms suppose that a number of samples of…

In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…

Support recovery of sparse signals from compressed linear measurements is a fundamental problem in compressed sensing (CS). In this paper, we study the orthogonal matching pursuit (OMP) algorithm for the recovery of support under noise. We…