Related papers: cuPDLPx: A Further Enhanced GPU-Based First-Order …

The Simplex tableau has been broadly used and investigated in the industry and academia. With the advent of the big data era, ever larger problems are posed to be solved in ever larger machines whose architecture type did not exist in the…

Linear programming (LP) relaxation is a standard technique for solving hard combinatorial optimization (CO) problems. Here we present a gradient descent algorithm which exploits the special structure of some LP relaxations induced by CO…

NVIDIA cuDNN is a low-level library that provides GPU kernels frequently used in deep learning. Specifically, cuDNN implements several equivalent convolution algorithms, whose performance and memory footprint may vary considerably,…

Computing with high-dimensional (HD) vectors, also referred to as $\textit{hypervectors}$, is a brain-inspired alternative to computing with scalars. Key properties of HD computing include a well-defined set of arithmetic operations on…

This paper introduces madupite, a high-performance distributed solver for large-scale Markov Decision Processes (MDPs). MDPs are widely used to model complex dynamical systems in various fields, including finance, epidemiology, and traffic…

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes.…

Motivated by big data applications, first-order methods have been extremely popular in recent years. However, naive gradient methods generally converge slowly. Hence, much efforts have been made to accelerate various first-order methods.…

Motivated by large-scale applications, there is a recent trend of research on using first-order methods for solving LP. Among them, PDLP, which is based on a primal-dual hybrid gradient (PDHG) algorithm, may be the most promising one. In…

In modern engineering scenarios, there is often a strict upper bound on the number of algorithm iterations that can be performed within a given time limit. This raises the question of optimal algorithmic configuration for a fixed and finite…

In high-performance computing, hotspot GPU kernels are primary bottlenecks, and expert manual tuning is costly and hard to port. Large language model methods often assume kernels can be compiled and executed cheaply, which fails in large…

We present a massively parallel Lagrange decomposition method for solving 0--1 integer linear programs occurring in structured prediction. We propose a new iterative update scheme for solving the Lagrangean dual and a perturbation technique…

Although deep models have been widely explored in solving partial differential equations (PDEs), previous works are primarily limited to data only with up to tens of thousands of mesh points, far from the million-point scale required by…

This paper investigates the convex optimization problem with general convex inequality constraints. To cope with this problem, a discrete-time algorithm, called augmented primal-dual gradient algorithm (Aug-PDG), is studied and analyzed. It…

A novel and scalable geometric multi-level algorithm is presented for the numerical solution of elliptic partial differential equations, specially designed to run with high occupancy of streaming processors inside Graphics Processing…

This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…

For large-scale graph analytics on the GPU, the irregularity of data access and control flow, and the complexity of programming GPUs have been two significant challenges for developing a programmable high-performance graph library.…

Implicit neural representations with multi-layer perceptrons (MLPs) have recently gained prominence for a wide variety of tasks such as novel view synthesis and 3D object representation and rendering. However, a significant challenge with…

To analyze large sets of grid states, e.g. when evaluating the impact from the uncertainties of the renewable generation with probabilistic Monte Carlo simulation or in stationary time series simulation, large number of power flow…

The Primal-Dual Hybrid Gradient (PDHG) algorithm is a first-order method that can exploit GPUs to solve large-scale linear programming problems. The approach can often be faster than the alternatives, simplex and interior-point methods,…

Symmetric linear solves are fundamental to a wide range of scientific and engineering applications, from climate modeling and structural analysis to machine learning and optimization. These workloads often rely on Cholesky (POTRF)…