相关论文: Convergence of the majorized PAM method with subsp…

This paper studies the problem of completing a low-rank matrix from a few of its random entries with the aid of prior information. We suggest a strategy to incorporate prior information into the standard matrix completion procedure by…

Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…

Tensor train (TT) factorization and corresponding TT rank, which can well express the low-rankness and mode correlations of higher-order tensors, have attracted much attention in recent years. However, TT factorization based methods are…

Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…

In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate…

This article is an extended version of previous work of the authors [40, 41] on low-rank matrix estimation in the presence of constraints on the factors into which the matrix is factorized. Low-rank matrix factorization is one of the basic…

This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are…

Low-rank matrix completion is a problem of immense practical importance. Recent works on the subject often use nuclear norm as a convex surrogate of the rank function. Despite its solid theoretical foundation, the convex version of the…

In this paper, we propose a novel solution for non-convex problems of multiple variables, especially for those typically solved by an alternating minimization (AM) strategy that splits the original optimization problem into a set of…

We present a numerical method for the minimization of constrained optimization problems where the objective is augmented with large quadratic penalties of inconsistent equality constraints. Such objectives arise from quadratic integral…

We develop computational methods for approximating the solution of a linear multi-term matrix equation in low rank. We follow an alternating minimization framework, where the solution is represented as a product of two matrices, and…

In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes…

Matrix decomposition is ubiquitous and has applications in various fields like speech processing, data mining and image processing to name a few. Under matrix decomposition, nonnegative matrix factorization is used to decompose a…

Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data recon- struction, and so on. We propose a new model to recover a low-rank tensor by simultaneously…

We show that proximal minimization algorithms (PMA), majorization minimization (MM), and alternating minimization (AM) are equivalent. Each type of algorithm leads to a decreasing sequence of objective function. New conditions on PMA are…

Stochastic approximation techniques play an important role in solving many problems encountered in machine learning or adaptive signal processing. In these contexts, the statistics of the data are often unknown a priori or their direct…

Local convergence analysis of the augmented Lagrangian method (ALM) is established for a large class of composite optimization problems with nonunique Lagrange multipliers under a second-order sufficient condition. We present a new…

We introduce SPRING, a novel stochastic proximal alternating linearized minimization algorithm for solving a class of non-smooth and non-convex optimization problems. Large-scale imaging problems are becoming increasingly prevalent due to…

Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…

This paper presents new variants of the averaged alternating modified reflections (AAMR) method for the best approximation problem. Under a mild constraint qualification, we first show its weak convergence and then establish a convergence…