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This work develops a proximal primal-dual decentralized strategy for multi-agent optimization problems that involve multiple coupled affine constraints, where each constraint may involve only a subset of the agents. The constraints are…

Optimization and Control · Mathematics 2019-12-12 Sulaiman A. Alghunaim , Kun Yuan , Ali H. Sayed

Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…

Statistics Theory · Mathematics 2009-09-03 Jinchi Lv , Yingying Fan

The goal of this paper is to find a low-rank approximation for a given tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP-hard problem. In this paper,…

Numerical Analysis · Mathematics 2016-10-20 Xiaofei Wang , Carmeliza Navasca

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…

Signal Processing · Electrical Eng. & Systems 2024-07-15 Dimitris Bertsimas , Nicholas A. G. Johnson

In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…

Optimization and Control · Mathematics 2024-05-08 Spyridon Pougkakiotis , Jacek Gondzio , Dionysis Kalogerias

Recent results in Compressive Sensing have shown that, under certain conditions, the solution to an underdetermined system of linear equations with sparsity-based regularization can be accurately recovered by solving convex relaxations of…

Computer Vision and Pattern Recognition · Computer Science 2012-01-19 Dheeraj Singaraju , Ehsan Elhamifar , Roberto Tron , Allen Y. Yang , S. Shankar Sastry

Recent hardware advancements in AI Accelerators and GPUs allow to efficiently compute sparse matrix multiplications, especially when 2 out of 4 consecutive weights are set to zero. However, this so-called 2:4 sparsity usually comes at a…

We describe an active-set method for the minimization of an objective function $\phi$ that is the sum of a smooth convex function and an $\ell_1$-regularization term. A distinctive feature of the method is the way in which active-set…

Optimization and Control · Mathematics 2015-05-19 Nitish Shirish Keskar , Jorge Nocedal , Figen Oztoprak , Andreas Waechter

Owing to their statistical properties, non-convex sparse regularizers have attracted much interest for estimating a sparse linear model from high dimensional data. Given that the solution is sparse, for accelerating convergence, a working…

Machine Learning · Computer Science 2021-10-22 Alain Rakotomamonjy , Rémi Flamary , Gilles Gasso , Joseph Salmon

Methods exploiting sparsity have been popular in imaging and signal processing applications including compression, denoising, and imaging inverse problems. Data-driven approaches such as dictionary learning and transform learning enable one…

Machine Learning · Computer Science 2018-02-05 Saiprasad Ravishankar , Anna Ma , Deanna Needell

The ever-increasing number of parameters in deep neural networks poses challenges for memory-limited applications. Regularize-and-prune methods aim at meeting these challenges by sparsifying the network weights. In this context we quantify…

Machine Learning · Computer Science 2018-10-30 Enzo Tartaglione , Skjalg Lepsøy , Attilio Fiandrotti , Gianluca Francini

In this paper, we show a way to exploit sparsity in the problem data in a primal-dual potential reduction method for solving a class of semidefinite programs. When the problem data is sparse, the dual variable is also sparse, but the primal…

Numerical Analysis · Mathematics 2025-10-20 Gun Srijuntongsiri , Stephen A. Vavasis

The sparse optimization problems arise in many areas of science and engineering, such as compressed sensing, image processing, statistical and machine learning. The $\ell_{0}$-minimization problem is one of such optimization problems, which…

Optimization and Control · Mathematics 2019-04-23 Jialiang Xu , Yun-Bin Zhao

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…

Machine Learning · Statistics 2015-06-05 Yiyuan She , Huanghuang Li , Jiangping Wang , Dapeng Wu

This paper presents a regularization technique incorporating a non-convex and non-smooth term, $\ell_{1}^{2}-\eta\ell_{2}^{2}$, with parameters $0<\eta\leq 1$ designed to address ill-posed linear problems that yield sparse solutions. We…

Optimization and Control · Mathematics 2025-06-16 Long Li , Liang Ding

Many regularization schemes for high-dimensional regression have been put forward. Most require the choice of a tuning parameter, using model selection criteria or cross-validation schemes. We show that a simple non-negative or…

Methodology · Statistics 2012-02-07 Nicolai Meinshausen

Given a set of response observations for a parametrized dynamical system, we seek a parametrized dynamical model that will yield uniformly small response error over a range of parameter values yet has low order. Frequently, access to…

Numerical Analysis · Mathematics 2018-08-20 Alexander Grimm , Christopher Beattie , Zlatko Drmač , Serkan Gugercin

We study a regularization framework that combines a convex fidelity term with multiple $\ell_1$-based regularizers, each linked to a distinct linear transform. This multi-penalty model enhances flexibility in promoting structured sparsity.…

Numerical Analysis · Mathematics 2026-02-02 Qianru Liu , Rui Wang , Yuesheng Xu

We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…

Information Theory · Computer Science 2011-09-29 Gilles Puy , Pierre Vandergheynst , Yves Wiaux

In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation regularization. The proposed…

Computer Vision and Pattern Recognition · Computer Science 2015-04-29 Chen Chen , Junzhou Huang , Lei He , Hongsheng Li