Related papers: Strong NP-Hardness for Sparse Optimization with Co…

We study the Compressed Sensing (CS) problem, which is the problem of finding the most sparse vector that satisfies a set of linear measurements up to some numerical tolerance. We introduce an $\ell_2$ regularized formulation of CS which we…

In this paper, we establish hardness and approximation results for various $L_p$-ball constrained homogeneous polynomial optimization problems, where $p \in [2,\infty]$. Specifically, we prove that for any given $d \ge 3$ and $p \in…

In this work we study convergence properties of sparse polynomial approximations for a class of affine parametric saddle point problems. Such problems can be found in many computational science and engineering fields, including the Stokes…

Measuring the error by an l^1-norm, we analyze under sparsity assumptions an l^0-regularization approach, where the penalty in the Tikhonov functional is complemented by a general stabilizing convex functional. In this context, ill-posed…

We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the…

High-dimensional sparse modeling with censored survival data is of great practical importance, as exemplified by modern applications in high-throughput genomic data analysis and credit risk analysis. In this article, we propose a class of…

This article proposes a sparse computation-based method for optimizing neural networks for reinforcement learning (RL) tasks. This method combines two ideas: neural network pruning and taking into account input data correlations; it makes…

The efficient sparse coding and reconstruction of signal vectors via linear observations has received a tremendous amount of attention over the last decade. In this context, the automated learning of a suitable basis or overcomplete…

We study the problem of minimizing a nonnegative separable concave function over a compact feasible set. We approximate this problem to within a factor of 1+epsilon by a piecewise-linear minimization problem over the same feasible set. Our…

Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on…

We propose a sparse regression method based on the non-concave penalized density power divergence loss function which is robust against infinitesimal contamination in very high dimensionality. Present methods of sparse and robust regression…

This paper deals with the non-uniqueness of the solutions of an analysis-Lasso regularization. Most of previous works in this area is concerned with the case where the solution set is a singleton, or to derive guarantees to enforce…

This paper considers the problem of signal denoising using a sparse tight-frame analysis prior. The L1 norm has been extensively used as a regularizer to promote sparsity; however, it tends to under-estimate non-zero values of the…

In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…

We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…

We continue the investigation of polynomial-time sparsification for NP-complete Boolean Constraint Satisfaction Problems (CSPs). The goal in sparsification is to reduce the number of constraints in a problem instance without changing the…

The explicit regularization and optimality of deep neural networks estimators from independent data have made considerable progress recently. The study of such properties on dependent data is still a challenge. In this paper, we carry out…

We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to Bayesian optimization: given an oracle that returns…

It was recently established that for convex optimization problems with sparse optimal solutions (be it entry-wise sparsity or matrix rank-wise sparsity) it is possible to design first-order methods with linear convergence rates that depend…

Many high dimensional sparse learning problems are formulated as nonconvex optimization. A popular approach to solve these nonconvex optimization problems is through convex relaxations such as linear and semidefinite programming. In this…