相关论文: I-LAMM for Sparse Learning: Simultaneous Control o…

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

We propose a new method of learning a sparse nonnegative-definite target matrix. Our primary example of the target matrix is the inverse of a population covariance or correlation matrix. The algorithm first estimates each column of the…

Fan and Li propose a family of variable selection methods via penalized likelihood using concave penalty functions. The nonconcave penalized likelihood estimators enjoy the oracle properties, but maximizing the penalized likelihood function…

Inexact proximal augmented Lagrangian methods (ipALMs) have been widely used for solving linearly constrained convex optimization problems, owing to their strong theoretical guarantees and excellent numerical performance. In practice,…

We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most existing types of nonconvex sparsity-inducing terms, bringing strong applicability to a…

In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…

Low-rank matrix approximation (LRMA) is a powerful technique for signal processing and pattern analysis. However, its potential for data compression has not yet been fully investigated in the literature. In this paper, we propose sparse…

For the general problem of minimizing a convex function over a compact convex domain, we will investigate a simple iterative approximation algorithm based on the method by Frank & Wolfe 1956, that does not need projection steps in order to…

Driven by recent advances in artificial intelligence (AI), a growing literature has demonstrated the potential for using large language models (LLMs) as scalable surrogates to generate human-like responses in many business applications. Two…

Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…

The L1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In…

The SparseStep algorithm is presented for the estimation of a sparse parameter vector in the linear regression problem. The algorithm works by adding an approximation of the exact counting norm as a constraint on the model parameters and…

We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized…

Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of…

In this paper, we propose a successive convex approximation framework for sparse optimization where the nonsmooth regularization function in the objective function is nonconvex and it can be written as the difference of two convex…

The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…

In [1], the distributed linear-quadratic problem with fixed communication topology (DFT-LQ) and the sparse feedback LQ problem (SF-LQ) are formulated into a nonsmooth and nonconvex optimization problem with affine constraints. Moreover, a…

In order to improve the performance of Least Mean Square (LMS) based system identification of sparse systems, a new adaptive algorithm is proposed which utilizes the sparsity property of such systems. A general approximating approach on…

Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…

We propose a simple modification to the iterative hard thresholding (IHT) algorithm, which recovers asymptotically sparser solutions as a function of the condition number. When aiming to minimize a convex function $f(x)$ with condition…