Related papers: Asynchronous Algorithms for Solving Linear Program…

In this paper, given a linear system of equations A x = b, we are finding locations in the plane to place objects such that sending waves from the source points and gathering them at the receiving points solves that linear system of…

It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.

Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…

This paper presents the first generic bi-objective binary linear branch-and-cut algorithm. Studying the impact of valid inequalities in solution and objective spaces, two cutting frameworks are proposed. The multi-point separation problem…

We describe an asynchronous parallel variant of the randomized Kaczmarz (RK) algorithm for solving the linear system $Ax=b$. The analysis shows linear convergence and indicates that nearly linear speedup can be expected if the number of…

We propose a new asynchronous parallel block-descent algorithmic framework for the minimization of the sum of a smooth nonconvex function and a nonsmooth convex one, subject to both convex and nonconvex constraints. The proposed framework…

This paper proposes a general formulation for temporal parallelisation of dynamic programming for optimal control problems. We derive the elements and associative operators to be able to use parallel scans to solve these problems with…

Many parallel algorithms which solve basic problems in computer science use auxiliary space linear in the input to facilitate conflict-free computation. There has been significant work on improving these parallel algorithms to be in-place,…

The aim of the paper is to introduce general techniques in order to optimize the parallel execution time of sorting on a distributed architectures with processors of various speeds. Such an application requires a partitioning step. For…

This report provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines. To illustrate the basic concepts and key issues,…

This paper presents a framework for designing a class of distributed, asynchronous optimization algorithms, realized as signal processing architectures utilizing various conservation principles. The architectures are specifically based on…

Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…

In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…

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…

We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local…

This paper takes an empirical look at asymptotic runtime growth rates for the most widely used algorithms for solving linear programming (LP) problems across a set of six optimization application areas that are known to produce large and…

We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…

We present an algorithm for the solution of a simultaneous space-time discretization of linear parabolic evolution equations with a symmetric differential operator in space. Building on earlier work, we recast this discretization into a…

This paper introduces the multiplicative variant of the recently proposed asynchronous additive coarse-space correction method. Definition of an asynchronous extension of multiplicative correction is not straightforward, however, our…

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…