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This note is concerned with the problem of minimizing a separable, convex, composite (smooth and nonsmooth) function subject to linear constraints. We study a randomized block-coordinate interpretation of the Chambolle-Pock primal-dual…
This study develops an algorithm for distributed computing of linear programming problems of huge-scales. Global consensus with single common variable, multiblocks, and augmented Lagrangian are adopted. The consensus is used to partition…
Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning. We present a blended matching pursuit algorithm, combining coordinate descent-like steps with stronger gradient descent steps, for…
The standard randomized sparse Kaczmarz (RSK) method is an algorithm to compute sparse solutions of linear systems of equations and uses sequential updates, and thus, does not take advantage of parallel computations. In this work, we…
This work provides the first convergence analysis for the Randomized Block Coordinate Descent method for minimizing a function that is both H\"older smooth and block H\"older smooth. Our analysis applies to objective functions that are…
Motivated by the randomized sketch to solve a variety of problems in scientific computation, we improve both the maximal weighted residual Kaczmarz method and the randomized block average Kaczmarz method using two new randomized sketch…
The randomized coordinate descent (RCD) method is a classical algorithm with simple, lightweight iterations that is widely used for various optimization problems, including the solution of positive semidefinite linear systems. As a linear…
In convolutional neural networks, the linear transformation of multi-channel two-dimensional convolutional layers with linear convolution is a block matrix with doubly Toeplitz blocks. Although a "wrapping around" operation can transform…
In the book [Meurant and Tichy, SIAM, 2024] we discussed the estimation of error norms in the conjugate gradient (CG) algorithm for solving linear systems $Ax=b$ with a symmetric positive definite matrix $A$, where $b$ and $x$ are vectors.…
Inhomogeneous dynamical mean-field theory has been employed to solve many interesting strongly interacting problems from transport in multilayered devices to the properties of ultracold atoms in a trap. The main computational step,…
In this paper, we develop RLOBPCG, an efficient method for computing a small number of singular triplets corresponding to the smallest singular values of large, tall matrices. The algorithm combines randomized preconditioner from the…
The randomized Kaczmarz method is an iterative algorithm that solves overdetermined systems of linear equations. Recently, the method was extended to systems of equalities and inequalities by Leventhal and Lewis. Even more recently, Needell…
Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale…
Block coordinate descent is an optimization paradigm that iteratively updates one block of variables at a time, making it quite amenable to big data applications due to its scalability and performance. Its convergence behavior has been…
Low-rank matrix approximation is one of the central concepts in machine learning, with applications in dimension reduction, de-noising, multivariate statistical methodology, and many more. A recent extension to LRMA is called low-rank…
Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…
This work presents a parallel variant of the algorithm introduced in [Acceleration of block coordinate descent methods with identification strategies Comput. Optim. Appl. 72(3):609--640, 2019] to minimize the sum of a partially separable…
The block coordinate descent (BCD) method is widely used for minimizing a continuous function f of several block variables. At each iteration of this method, a single block of variables is optimized, while the remaining variables are held…
This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, and…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…