Related papers: An algorithm for non-convex off-the-grid sparse sp…

We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth…

We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…

A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading…

In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…

An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for…

This paper presents novel cascaded channel estimation techniques for an intelligent reflecting surface-aided multiple-input multiple-output system. Motivated by the channel angular sparsity at higher frequency bands, the channel estimation…

In this paper, we study a new notion of scaled minimaxity for sparse estimation in high-dimensional linear regression model. We present more optimistic lower bounds than the one given by the classical minimax theory and hence improve on…

Compressed sensing is a theory which guarantees the exact recovery of sparse signals from a small number of linear projections. The sampling schemes suggested by current compressed sensing theories are often of little practical relevance…

We introduce SPRING, a novel stochastic proximal alternating linearized minimization algorithm for solving a class of non-smooth and non-convex optimization problems. Large-scale imaging problems are becoming increasingly prevalent due to…

In many applications in compressed sensing, the measurement matrix is a Fourier matrix, i.e., it measures the Fourier transform of the underlying signal at some specified `base' frequencies $\{u_i\}_{i=1}^M$, where $M$ is the number of…

This paper is concerned with the fundamental problem of estimating chirp parameters from a mixture of linear chirp signals. Unlike most previous methods, which solve the problem by discretizing the parameter space and then estimating the…

We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…

In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is…

We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…

A sparse modeling approach is proposed for analyzing scanning tunneling microscopy topography data, which contains numerous peaks corresponding to surface atoms. The method, based on the relevance vector machine with $\mathrm{L}_1$…

We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank…

We study the problem of estimating multiple predictive functions from a dictionary of basis functions in the nonparametric regression setting. Our estimation scheme assumes that each predictive function can be estimated in the form of a…

This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…