1 citations · 2 across the 18 of their papers we have counts for
20 papers
H-PDLP: GPU-Accelerated Linear Programming via Generalized PDHG and Homogeneous Self-Dual Embedding
Haihao Lu, Bo Tang
GPU-based first-order methods are emerging as an approach for solving large-scale linear programming (LP) problems. We present H-PDLP, a GPU first-order LP solver based on a genera…
PDNQP: A GPU-based Factorization-free Method for Large-scale Nonconvex Quadratic Programming
Zixi Chen, Haihao Lu
Large-scale nonconvex quadratic programming remains challenging because the sparse matrix factorizations used by many existing solvers can incur substantial computational and memor…
On the Local Linear Convergence of Operator Splitting Methods for Conic Programming
Lijun Ding, Haihao Lu, Jinwen Yang
Operator-splitting methods such as the primal-dual hybrid gradient method (PDHG) and the alternating direction method of multipliers (ADMM) often exhibit linear convergence on coni…
FlashFolio: A GPU-Accelerated Solver for Portfolio Optimization
Yilun Jiang, Haihao Lu, Zedong Peng +1
We present FlashFolio, a GPU-accelerated solver for single-period and multi-period portfolio optimization with factor-based risk modeling, bid-offer spread costs, and nonlinear mar…
End-to-End Learning of Correlated Operating Reserve Requirements in Security-Constrained Economic Dispatch
Owen Shen, Hung-po Chao, Haihao Lu +1
Operating reserve requirements in security-constrained economic dispatch (SCED) depend strongly on the assumed correlation structure of renewable forecast errors, yet that structur…
Active set identification and rapid convergence for degenerate primal-dual problems
Mateo Díaz, Pedro Izquierdo Lehmann, Haihao Lu +1
Primal-dual methods for solving convex optimization problems with functional constraints often exhibit a distinct two-stage behavior. Initially, they converge towards a solution at…
cuPDLPx: A Further Enhanced GPU-Based First-Order Solver for Linear Programming
Haihao Lu, Zedong Peng, Jinwen Yang
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…
Enhanced PDHG for Linear Programming with Online Preconditioning
Haihao Lu, Wanyu Zhang
We present an online preconditioning technique for the primal-dual hybrid gradient (PDHG) algorithm for linear programming (LP). The method adaptively updates primal and dual preco…
An Overview of GPU-based First-Order Methods for Linear Programming and Extensions
Haihao Lu, Jinwen Yang
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 re…
New Understandings and Computation on Augmented Lagrangian Methods for Low-Rank Semidefinite Programming
Lijun Ding, Haihao Lu, Jinwen Yang
Augmented Lagrangian Method (ALM) combined with Burer-Monteiro (BM) factorization, dubbed ALM-BM, offers a powerful approach for solving large-scale low-rank semidefinite programs…
PDLP: A Practical First-Order Method for Large-Scale Linear Programming
David Applegate, Mateo Díaz, Oliver Hinder +4
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) metho…
MPAX: Mathematical Programming in JAX
Haihao Lu, Zedong Peng, Jinwen Yang
We present MPAX (Mathematical Programming in JAX), an open-source first-order solver for large-scale linear programming (LP) and convex quadratic programming (QP) built natively in…
PDOT: a Practical Primal-Dual Algorithm and a GPU-Based Solver for Optimal Transport
Haihao Lu, Jinwen Yang
In this paper, we propose a practical primal-dual algorithm with theoretical guarantees and develop a GPU-based solver, which we dub PDOT, for solving large-scale optimal transport…
Restarted Halpern PDHG for Linear Programming
Haihao Lu, Jinwen Yang
In this paper, we propose and analyze a new matrix-free primal-dual algorithm, called restarted Halpern primal-dual hybrid gradient (rHPDHG), for solving linear programming (LP). W…
First-Order Methods for Linear Programming
Haihao Lu
Linear programming is the seminal optimization problem that has spawned and grown into today's rich and diverse optimization modeling and algorithmic landscape. This article provid…
cuPDLP-C: A Strengthened Implementation of cuPDLP for Linear Programming by C language
Haihao Lu, Jinwen Yang, Haodong Hu +6
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…
Achieving Fairness and Accuracy in Regressive Property Taxation
Ozan Candogan, Feiyu Han, Haihao Lu
Regressivity in property taxation, or the disproportionate overassessment of lower-valued properties compared to higher-valued ones, results in an unfair taxation burden for Americ…
cuPDLP.jl: A GPU Implementation of Restarted Primal-Dual Hybrid Gradient for Linear Programming in Julia
Haihao Lu, Jinwen Yang
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 restarte…
A Practical and Optimal First-Order Method for Large-Scale Convex Quadratic Programming
Haihao Lu, Jinwen Yang
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 me…
On the Convergence of L-shaped Algorithms for Two-Stage Stochastic Programming
John R. Birge, Haihao Lu, Baoyu Zhou
In this paper, we design, analyze, and implement a variant of the two-loop L-shaped algorithms for solving two-stage stochastic programming problems that arise from important appli…