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In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…
Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…
Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach…
We consider a class of structured, nonconvex, nonsmooth optimization problems under orthogonality constraints, where the objectives combine a smooth function, a nonsmooth concave function, and a nonsmooth weakly convex function. This class…
Recently, low-rank tensor completion has become increasingly attractive in recovering incomplete visual data. Considering a color image or video as a three-dimensional (3D) tensor, existing studies have put forward several definitions of…
To analyze the abundance of multidimensional data, tensor-based frameworks have been developed. Traditionally, the matrix singular value decomposition (SVD) is used to extract the most dominant features from a matrix containing the…
The recently proposed fully-connected tensor network (FCTN) decomposition has demonstrated significant advantages in correlation characterization and transpositional invariance, and has achieved notable achievements in multi-dimensional…
Currently, low-rank tensor completion has gained cumulative attention in recovering incomplete visual data whose partial elements are missing. By taking a color image or video as a three-dimensional (3D) tensor, previous studies have…
In real-world scenarios, complex data such as multispectral images and multi-frame videos inherently exhibit robust low-rank property. This property is vital for multi-dimensional inverse problems, such as tensor completion, spectral…
We consider convex relaxations for recovering low-rank tensors based on constrained minimization over a ball induced by the tensor nuclear norm, recently introduced in \cite{tensor_tSVD}. We build on a recent line of results that considered…
In this paper, we consider the tensor completion problem, which has many researchers in the machine learning particularly concerned. Our fast and precise method is built on extending the $L_{2,1}$-norm minimization and Qatar Riyal…
This paper addresses the problem of efficiently classifying high-dimensional data over decentralized networks. Penalized support vector machines (SVMs) are widely used for high-dimensional classification tasks. However, the double…
In this paper, we propose a new unified optimization algorithm for general tensor decomposition which is formulated as an inverse problem for low-rank tensors in the general linear observation models. The proposed algorithm supports three…
Alternating direction method of multipliers (ADMM) is a popular optimization tool for the composite and constrained problems in machine learning. However, in many machine learning problems such as black-box attacks and bandit feedback, ADMM…
We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel…
In this paper, we develop a symmetric accelerated stochastic Alternating Direction Method of Multipliers (SAS-ADMM) for solving separable convex optimization problems with linear constraints. The objective function is the sum of a possibly…
Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…
This paper introduces a novel approach to solving multi-block nonconvex composite optimization problems through a proximal linearized Alternating Direction Method of Multipliers (ADMM). This method incorporates an Increasing Penalization…
In this paper, we propose and analyze an inexact version of the symmetric proximal alternating direction method of multipliers (ADMM) for solving linearly constrained optimization problems. Basically, the method allows its first subproblem…
This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…