相关论文: On the Relationships among GPU-Accelerated First-O…

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…

We introduce cuPDLPx, a further enhanced GPU-based first-order solver for linear programming. Building on the recently developed restarted Halpern PDHG for LP, cuPDLPx incorporates a number of new techniques, including a new restart…

In this paper, we introduce an HPR-LP solver, an implementation of a Halpern Peaceman-Rachford (HPR) method with semi-proximal terms for solving linear programming (LP). The HPR method enjoys the iteration complexity of $O(1/k)$ in terms of…

Linear Programming (LP) is a foundational optimization technique with widespread applications in finance, energy trading, and supply chain logistics. However, traditional Central Processing Unit (CPU)-based LP solvers often struggle to meet…

Recent research has focused on developing GPU-accelerated first-order solvers for linear programming (LP). This line of work, however, has largely overlooked the role of presolving, and thus prior results do not fully reflect the speedups…

We present a batched first-order method for solving multiple linear programs in parallel on GPUs. Our approach extends the primal-dual hybrid gradient algorithm to efficiently solve batches of related linear programming problems that arise…

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…

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…

Linear Programs (LPs) appear in a large number of applications and offloading them to a GPU is viable to gain performance. Existing work on offloading and solving an LP on a GPU suggests that there is performance gain generally on large…

A recent GPU implementation of the Restarted Primal-Dual Hybrid Gradient Method for Linear Programming was proposed in Lu and Yang (2023). Its computational results demonstrate the significant computational advantages of the GPU-based…

In this paper, we introduce HPR-QP, a dual Halpern Peaceman-Rachford (HPR) method designed for solving large-scale convex composite quadratic programming. One distinctive feature of HPR-QP is that, instead of working with the primal…

We present PDLP, a practical first-order method for linear programming (LP) designed to solve large-scale LP problems. PDLP is based on the primal-dual hybrid gradient (PDHG) method applied to the minimax formulation of LP. PDLP…

Linear Programs (LPs) appear in a large number of applications and offloading them to the GPU is viable to gain performance. Existing work on offloading and solving an LP on GPU suggests that performance is gained from large sized LPs…

First-order methods based on the PDHG algorithm have recently emerged as a viable option for efficiently solving large-scale linear programming problems. One highly desirable property of these methods is that they can make effective use of…

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…

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),…

Security-Constrained Unit Commitment is a fundamental optimization problem in power systems operations. The primary computational bottleneck arises from the need to solve large-scale Linear Programming (LP) relaxations within…

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…

We introduce a fusion of GPU accelerated primal heuristics for Mixed Integer Programming. Leveraging GPU acceleration enables exploration of larger search regions and faster iterations. A GPU-accelerated PDLP serves as an approximate LP…

There has been a recent surge in development of first-order methods (FOMs) for solving huge-scale linear programming (LP) problems. The attractiveness of FOMs for LP stems in part from the fact that they avoid costly matrix factorization…