Related papers: Asynchronous Richardson iterations
The alternating direction method of multipliers (ADMM) has been recognized as a versatile approach for solving modern large-scale machine learning and signal processing problems efficiently. When the data size and/or the problem dimension…
This paper presents an asynchronous incremental aggregated gradient algorithm and its implementation in a parameter server framework for solving regularized optimization problems. The algorithm can handle both general convex (possibly…
This paper first proposes an N-block PCPM algorithm to solve N-block convex optimization problems with both linear and nonlinear constraints, with global convergence established. A linear convergence rate under the strong second-order…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
The initialization of equation-based differential-algebraic system models, and more in general the solution of many engineering and scientific problems, require the solution of systems of nonlinear equations. Newton-Raphson's method is…
Various first order approaches have been proposed in the literature to solve Linear Programming (LP) problems, recently leading to practically efficient solvers for large-scale LPs. From a theoretical perspective, linear convergence rates…
Asynchronous programming has appeared as a programming style that overcomes undesired properties of concurrent programming. Typically in asynchronous models of programming, methods are posted into a post list for latter execution. The order…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
Markov Chain Monte Carlo (MCMC) methods such as Gibbs sampling are finding widespread use in applied statistics and machine learning. These often lead to difficult computational problems, which are increasingly being solved on parallel and…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
We present a numerical method for convergence acceleration for multifidelity models of parameterized ordinary differential equations. The hierarchy of models is defined as trajectories computed using different timesteps in a time…
Asynchronous-parallel algorithms have the potential to vastly speed up algorithms by eliminating costly synchronization. However, our understanding to these algorithms is limited because the current convergence of asynchronous (block)…
To design efficient parallel algorithms, some recent papers showed that many sequential iterative algorithms can be directly parallelized but there are still challenges in achieving work-efficiency and high-parallelism. Work-efficiency can…
The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
An algorithm is discussed for converting a class of recursive processes to a parallel system. It is argued that this algorithm can be superior to certain methods currently found in the literature for an important subset of problems. The…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
In this note, following suggestions by Tao, we extend the randomized algorithm for linear equations over prime fields by Raghavendra to a randomized algorithm for linear equations over the reals. We also show that the algorithm can be…
We study sequential multiple testing with independent data streams, where the goal is to identify an unknown subset of signals while controlling commonly used error metrics, including generalized familywise rates and false discovery and…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…