Related papers: Batched First-Order Methods for Parallel LP Solvin…

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,…

Convex quadratic programming (QP) is an important class of optimization problem with wide applications in practice. The classic QP solvers are based on either simplex or barrier method, both of which suffer from the scalability issue…

We present PDLP, a practical first-order method for linear programming (LP) that can solve to the high levels of accuracy that are expected in traditional LP applications. In addition, it can scale to very large problems because its core…

Integer sorting on multicores and GPUs can be realized by a variety of approaches that include variants of distribution-based methods such as radix-sort, comparison-oriented algorithms such as deterministic regular sampling and random…

Process mapping asks to assign vertices of a task graph to processing elements of a supercomputer such that the computational workload is balanced while the communication cost is minimized. Motivated by the recent success of GPU-based graph…

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…

Finding the most probable (MAP) model in SRL frameworks such as Markov logic and Problog can, in principle, be solved by encoding the problem as a `grounded-out' mixed integer program (MIP). However, useful first-order structure disappears…

In this paper we present a methodology for data accesses when solving batches of Tridiagonal and Pentadiagonal matrices that all share the same left-hand-side (LHS) matrix. The intended application is to the numerical solution of Partial…

Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…

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…

We present GFORS, a GPU-accelerated framework for large binary integer programs. It couples a first-order (PDHG-style) routine that guides the search in the continuous relaxation with a randomized, feasibility-aware sampling module that…

We study the problem of executing an application represented by a precedence task graph on a parallel machine composed of standard computing cores and accelerators. Contrary to most existing approaches, we distinguish the allocation and the…

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…

In this paper, we introduce a practical GPU-enhanced matrix-free first-order method for solving large-scale conic programming problems, which we refer to as PDCS, standing for the Primal-Dual Conic Programming Solver. Problems that it…

We present a mixed-integer programming (MIP) model for scheduling quantum circuits to minimize execution time. Our approach maximizes parallelism by allowing non-overlapping gates (those acting on distinct qubits) to execute simultaneously.…

Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an…

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…

The exponential growth of computational workloads is surpassing the capabilities of conventional architectures, which are constrained by fundamental limits. In-memory computing (IMC) with RRAM provides a promising alternative by providing…

We investigate the use of low-precision first-order methods (FOMs) within a fix-and-propagate (FP) framework for solving mixed-integer programming problems (MIPs). We employ GPU-accelerated PDLP, a variant of the Primal-Dual Hybrid Gradient…

Large-scale competitive market equilibrium problems arise in a wide range of important applications, including economic decision-making and intelligent manufacturing. Traditional solution methods, such as interior-point algorithms and…