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We present an efficient, robust and fully GPU-accelerated aggregation-based algebraic multigrid preconditioning technique for the solution of large sparse linear systems. These linear systems arise from the discretization of elliptic PDEs.…

Numerical Analysis · Mathematics 2014-03-10 Rajesh Gandham , Ken Esler , Yongpeng Zhang

Energy system optimization models are increasing in scope and resolution, yielding large and challenging linear programs. For a long time, the standard way to address such problems has relied on shared-memory interior-point methods (IPM),…

Optimization and Control · Mathematics 2026-05-07 Janina Zittel , Annika Buchholz , Michael Bussieck , Frederik Fiand , Thorsten Koch , Lukas Mehl , Niels Lindner , Manuel Wetzel

Memory bound applications such as solvers for large sparse systems of equations remain a challenge for GPUs. Fast solvers should be based on numerically efficient algorithms and implemented such that global memory access is minimised. To…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-06-01 Eike Hermann Müller , Robert Scheichl , Eero Vainikko

Parallel computing can offer an enormous advantage regarding the performance for very large applications in almost any field: scientific computing, computer vision, databases, data mining, and economics. GPUs are high performance many-core…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-11-24 Bogdan Oancea , Tudorel Andrei , Raluca Mariana Dragoescu

In this paper, we provide an affirmative answer to the long-standing question: Are GPUs useful in solving linear programming? We present cuPDLP.jl, a GPU implementation of restarted primal-dual hybrid gradient (PDHG) for solving linear…

Optimization and Control · Mathematics 2024-06-10 Haihao Lu , Jinwen Yang

We present the design and optimization of a linear solver on General Purpose GPUs for the efficient and high-throughput evaluation of the marginalized graph kernel between pairs of labeled graphs. The solver implements a preconditioned…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-05-20 Yu-Hang Tang , Oguz Selvitopi , Doru Popovici , Aydın Buluç

Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set…

Optimization and Control · Mathematics 2007-05-23 Steven J. Benson , Todd S. Munson

The efficient solution of large sparse saddle point systems is very important in computational fluid mechanics. The discontinuous Galerkin finite element methods have become increasingly popular for incompressible flow problems but their…

Mathematical Software · Computer Science 2021-01-18 Denis Demidov , Lin Mu , Bin Wang

The past decade has witnessed a dramatic acceleration of lattice quantum chromodynamics calculations in nuclear and particle physics. This has been due to both significant progress in accelerating the iterative linear solvers using…

High Energy Physics - Lattice · Physics 2016-12-26 M. A. Clark , Bálint Joó , Alexei Strelchenko , Michael Cheng , Arjun Gambhir , Richard Brower

This manuscript presents a new extended linear system for integral equation based techniques for solving boundary value problems on locally perturbed geometries. The new extended linear system is similar to a previously presented technique…

Numerical Analysis · Mathematics 2021-03-17 Yabin Zhang , Adrianna Gillman

The solution of a sparse system of linear equations is ubiquitous in scientific applications. Iterative methods, such as the Preconditioned Conjugate Gradient method (PCG), are normally chosen over direct methods due to memory and…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-03-04 Joshua Dennis Booth , Hongyang Sun , Trevor Garnett

While linear programming (LP) decoding provides more flexibility for finite-length performance analysis than iterative message-passing (IMP) decoding, it is computationally more complex to implement in its original form, due to both the…

Information Theory · Computer Science 2009-02-05 Mohammad H. Taghavi , Amin Shokrollahi , Paul H. Siegel

The two-dimensional layout optimization problem reinforced by the efficient space utilization demand has a wide spectrum of practical applications. Formulating the problem as a nonlinear minimization problem under planar equality and/or…

Data Structures and Algorithms · Computer Science 2009-02-19 Dorit Ron , Ilya Safro , Achi Brandt

As renewable energy integration, sector coupling, and spatiotemporal detail increase, energy system optimization models grow in size and complexity, often pushing solvers to their performance limits. This systematic review explores…

The rapid progress in GPU computing has revolutionized many fields, yet its potential in mathematical programming, such as linear programming (LP), has only recently begun to be realized. This survey aims to provide a comprehensive overview…

Optimization and Control · Mathematics 2025-06-04 Haihao Lu , Jinwen Yang

Constrained optimization problems arise frequently in classical machine learning. There exist frameworks addressing constrained optimization, for instance, CVXPY and GENO. However, in contrast to deep learning frameworks, GPU support is…

Machine Learning · Computer Science 2022-03-31 Sören Laue , Mark Blacher , Joachim Giesen

In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware…

Optimization and Control · Mathematics 2019-08-05 Ambros Gleixner , Nils-Christian Kempke , Thorsten Koch , Daniel Rehfeldt , Svenja Uslu

In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…

Numerical Analysis · Mathematics 2022-03-17 Takeshi Iwashita , Kota Ikehara , Takeshi Fukaya , Takeshi Mifune

Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…

Numerical Analysis · Mathematics 2014-07-02 Nam Nguyen , Deanna Needell , Tina Woolf

We present a GPU-accelerated version of a high-order discontinuous Galerkin discretization of the unsteady incompressible Navier-Stokes equations. The equations are discretized in time using a semi-implicit scheme with explicit treatment of…

Numerical Analysis · Mathematics 2018-05-08 Ali Karakus , Noel Chalmers , Kasia Swirydowicz , Timothy Warburton