Related papers: A Lagrange-Newton Algorithm for Sparse Nonlinear P…
In this paper we present a linear programming solution for sign pattern recovery of a sparse signal from noisy random projections of the signal. We consider two types of noise models, input noise, where noise enters before the random…
Support vector machine (SVM) has proved to be a successful approach for machine learning. Two typical SVM models are the L1-loss model for support vector classification (SVC) and $\epsilon$-L1-loss model for support vector regression (SVR).…
Numerous practical medical problems often involve data that possess a combination of both sparse and non-sparse structures. Traditional penalized regularizations techniques, primarily designed for promoting sparsity, are inadequate to…
Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
The doubly nonnegative (DNN) cone, being the set of all positive semidefinite matrices whose elements are nonnegative, is a popular approximation of the computationally intractable completely positive cone. The major difficulty for…
Random classical codes have good error correcting properties, and yet they are notoriously hard to decode in practice. Despite many decades of extensive study, the fastest known algorithms still run in exponential time. The Learning Parity…
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…
This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a…
Sparse signal recovery is one of the most fundamental problems in various applications, including medical imaging and remote sensing. Many greedy algorithms based on the family of hard thresholding operators have been developed to solve the…
Undirected graphical models have been especially popular for learning the conditional independence structure among a large number of variables where the observations are drawn independently and identically from the same distribution.…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
This paper addresses the problem of scalable optimization for L1-regularized conditional Gaussian graphical models. Conditional Gaussian graphical models generalize the well-known Gaussian graphical models to conditional distributions to…
We present an analysis of the Locally Competitive Algorithm (LCA), a Hopfield-style neural network that efficiently solves sparse approximation problems (e.g., approximating a vector from a dictionary using just a few non-zero…
This work focuses on a class of general decentralized constraint-coupled optimization problems. We propose a novel nested primal-dual gradient algorithm (NPGA), which can achieve linear convergence under the weakest known condition, and its…
We consider a class of $\ell_0$-regularized linear-quadratic (LQ) optimal control problems. This class of problems is obtained by augmenting a penalizing sparsity measure to the cost objective of the standard linear-quadratic regulator…
The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…
In this paper we study a constraint-based representation of neural network architectures. We cast the learning problem in the Lagrangian framework and we investigate a simple optimization procedure that is well suited to fulfil the…
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…