Related papers: An Augmented Lagrangian Method-Based Framework in …
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.…
This paper proposes a systematic mathematical analysis of both the direct and inverse acoustic scattering problem given the source in Radon measure space. For the direct problem, we investigate the well-posedness including the existence,…
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,…
Multi-task learning enhances model generalization by jointly learning from related tasks. This paper focuses on the $\ell_{1,\infty}$-norm constrained multi-task learning problem, which promotes a shared feature representation while…
This paper is devoted to studying an augmented Lagrangian method for solving a class of manifold optimization problems, which have nonsmooth objective functions and nonlinear constraints. Under the constant positive linear dependence…
We propose an efficient algorithm for sparse signal reconstruction problems. The proposed algorithm is an augmented Lagrangian method based on the dual sparse reconstruction problem. It is efficient when the number of unknown variables is…
We develop a fast and robust algorithm for solving large scale convex composite optimization models with an emphasis on the $\ell_1$-regularized least squares regression (Lasso) problems. Despite the fact that there exist a large number of…
This paper proposes a novel distributed semismooth Newton based augmented Lagrangian method for solving a class of optimization problems over networks, where the global objective is defined as the sum of locally held cost functions, and…
The sparse group Lasso is a widely used statistical model which encourages the sparsity both on a group and within the group level. In this paper, we develop an efficient augmented Lagrangian method for large-scale non-overlapping sparse…
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…
We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…
In this paper, we develop a novel primal-dual semismooth Newton method for solving linearly constrained multi-block convex composite optimization problems. First, a differentiable augmented Lagrangian (AL) function is constructed by…
In this paper, we develop and numerically implement a novel approach for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the…
This paper is concerned with a partially linear semiparametric regression model containing an unknown regression coefficient, an unknown nonparametric function, and an unobservable Gaussian distributed random error. We focus on the case of…
Square-root Lasso problems are proven robust regression problems. Furthermore, square-root regression problems with structured sparsity also plays an important role in statistics and machine learning. In this paper, we focus on the…
We present a proximal augmented Lagrangian based solver for general convex quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case…
In applying the level-set method developed in [Van den Berg and Friedlander, SIAM J. on Scientific Computing, 31 (2008), pp.~890--912 and SIAM J. on Optimization, 21 (2011), pp.~1201--1229] to solve the fused lasso problems, one needs to…
Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…
The method of superposition is proposed in combination with a sparse $\ell_1$ optimisation algorithm with the aim of finding a sparse basis to accurately reconstruct the structural vibrations of a radiating object from a set of acoustic…
The octagonal shrinkage and clustering algorithm for regression (OSCAR), equipped with the $\ell_1$-norm and a pair-wise $\ell_{\infty}$-norm regularizer, is a useful tool for feature selection and grouping in high-dimensional data…