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Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…

Computation · Statistics 2022-11-02 Qian LI , Binyan Jiang , Defeng Sun

Inference by means of mathematical modeling from a collection of observations remains a crucial tool for scientific discovery and is ubiquitous in application areas such as signal compression, imaging restoration, and supervised machine…

Numerical Analysis · Mathematics 2022-07-19 Matthias Chung , Rosemary Renaut

We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an $\ell_2$ data-fidelity term and a…

Optimization and Control · Mathematics 2015-05-14 Manya V. Afonso , José M. Bioucas-Dias , Mário A. T. Figueiredo

Augmented Lagrangian method (also called as method of multipliers) is an important and powerful optimization method for lots of smooth or nonsmooth variational problems in modern signal processing, imaging, optimal control and so on.…

Optimization and Control · Mathematics 2021-08-31 Hongpeng Sun

We provide a simplified form of Primal Augmented Lagrange Multiplier algorithm. We intend to fill the gap in the steps involved in the mathematical derivations of the algorithm so that an insight into the algorithm is made. The experiment…

Numerical Analysis · Computer Science 2014-01-02 B. Premjith , S. Sachin Kumar , Akhil Manikkoth , T V Bijeesh , K P Soman

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

Numerical Analysis · Mathematics 2025-06-16 Jianchao Bai , Linyuan Jia , Zheng Peng

We implement an Augmented Lagrangian method to minimize a constrained least-squares cost function designed to find polyadic decompositions of the matrix multiplication tensor. We use this method to obtain new discrete decompositions and…

Numerical Analysis · Mathematics 2023-10-05 Charlotte Vermeylen , Marc Van Barel

Sparsity-based methods are widely used in machine learning, statistics, and signal processing. There is now a rich class of structured sparsity approaches that expand the modeling power of the sparsity paradigm and incorporate constraints…

Data Structures and Algorithms · Computer Science 2017-12-22 Aleksander Mądry , Slobodan Mitrović , Ludwig Schmidt

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…

Optimization and Control · Mathematics 2012-10-10 Manya V. Afonso , José M. Bioucas-Dias , Mário A. T. Figueiredo

We study the problem of recovering the underlining sparse signals from clean or noisy phaseless measurements. Due to the sparse prior of signals, we adopt an L0regularized variational model to ensure only a small number of nonzero elements…

Optimization and Control · Mathematics 2016-12-09 Yuping Duan , Chunlin Wu , Zhi-Feng Pang , Huibin Chang

In this paper, we propose a penalty dual-primal augmented lagrangian method for solving convex minimization problems under linear equality or inequality constraints. The proposed method combines a novel penalty technique with updates the…

Optimization and Control · Mathematics 2023-05-09 Jie Liu , Xiaoqing Ou , Jiawei Chen

Support vector machines (SVMs) are successful modeling and prediction tools with a variety of applications. Previous work has demonstrated the superiority of the SVMs in dealing with the high dimensional, low sample size problems. However,…

Optimization and Control · Mathematics 2021-02-04 Dunbiao Niu , Chengjing Wang , Peipei Tang , Qingsong Wang , Enbin Song

Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…

Numerical Analysis · Mathematics 2017-05-23 Richard C. Barnard , Rick Archibald

We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…

Numerical Analysis · Computer Science 2009-01-08 Wei Dai , Olgica Milenkovic

In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optimization problem, the basis to decompose the signal is not…

Information Theory · Computer Science 2014-10-14 Thomas Y. Hou , Zuoqiang Shi

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…

Optimization and Control · Mathematics 2025-03-04 Lahcen El Bourkhissi , Ion Necoara , Panagiotis Patrinos , Quoc Tran-Dinh

We derive a memory-efficient first-order variable splitting algorithm for convex image reconstruction problems with non-smooth regularization terms. The algorithm is based on a primal-dual approach, where one of the dual variables is…

Optimization and Control · Mathematics 2019-04-02 Greg Ongie , Naveen Murthy , Laura Balzano , Jeffrey A. Fessler

We develop a decomposition method based on the augmented Lagrangian framework to solve a broad family of semidefinite programming problems, possibly with nonlinear objective functions, nonsmooth regularization, and general linear…

Optimization and Control · Mathematics 2023-03-08 Yifei Wang , Kangkang Deng , Haoyang Liu , Zaiwen Wen

In this work we reformulate the method presented in App. Opt. 53:2297 (2014) as a constrained minimization problem using the augmented Lagrangian method. First we introduce the new method and then describe the numerical solution, which…

Numerical Analysis · Mathematics 2020-08-21 Ricardo Legarda-Saenz , Carlos Brito-Loeza

Common problem in signal processing is reconstruction of the missing signal samples. Missing samples can occur by intentionally omitting signal coefficients to reduce memory requirements, or to speed up the transmission process. Also, noisy…

Information Theory · Computer Science 2015-03-02 Slavoljub Jokić , Ljindita Niković , Jelena Kadović