相关论文: A subspace-accelerated split Bregman method for sp…

Aggregation equations are broadly used to model population dynamics with nonlocal interactions, characterized by a potential in the equation. This paper considers the inverse problem of identifying the potential from a single noisy…

We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…

This paper is devoted to the study of acceleration methods for an inequality constrained convex optimization problem by using Lyapunov functions. We first approximate such a problem as an unconstrained optimization problem by employing the…

This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear…

The problem of finding sparse solutions to underdetermined systems of linear equations arises in several applications (e.g. signal and image processing, compressive sensing, statistical inference). A standard tool for dealing with sparse…

We present and analyze a novel sparse polynomial technique for approximating high-dimensional Hilbert-valued functions, with application to parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our…

In this paper, we explore a specific optimization problem that involves the combination of a differentiable nonconvex function and a nondifferentiable function. The differentiable component lacks a global Lipschitz continuous gradient,…

We propose an inference method to estimate sparse interactions and biases according to Boltzmann machine learning. The basis of this method is $L_1$ regularization, which is often used in compressed sensing, a technique for reconstructing…

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…

We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The convergence is established using the notion of variable quasi-Bregman monotone…

This article considers constrained $\ell_1$ minimization methods for the recovery of high dimensional sparse signals in three settings: noiseless, bounded error and Gaussian noise. A unified and elementary treatment is given in these noise…

Sparse training reduces the memory and computational costs of deep neural networks. However, sparse optimization methods, e.g., those adding an $\ell_1$ penalty, often control sparsity only indirectly through a regularization parameter…

A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…

In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…

The de-facto standard approach of promoting sparsity by means of $\ell_1$-regularization becomes ineffective in the presence of simplex constraints, i.e.,~the target is known to have non-negative entries summing up to a given constant. The…

Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of applications in machine learning, data science and statistics. Classically, such problems are solved via…

Coherent X-ray photons with energies higher than 50 keV offer new possibilities for imaging nanoscale lattice distortions in bulk crystalline materials using Bragg peak phase retrieval methods. However, the compression of reciprocal space…

Permutation synchronization is an important problem in computer science that constitutes the key step of many computer vision tasks. The goal is to recover $n$ latent permutations from their noisy and incomplete pairwise measurements. In…

Sparse hyperspectral unmixing from large spectral libraries has been considered to circumvent limitations of endmember extraction algorithms in many applications. This strategy often leads to ill-posed inverse problems, which can benefit…

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…