cuPDQPx: A GPU-Accelerated Restarted Halpern PDHG for Large-Scale Convex Quadratic Programming
Abstract
We present cuPDQPx, a GPU-accelerated, factorization-free first-order solver for large-scale convex quadratic programming (QP). Building on the restarted reflected Halpern primal-dual framework of cuPDLPx, we introduce an auxiliary-variable splitting that yields explicit updates without linearizing the quadratic objective or solving inner quadratic subproblems. A preconditioned proximal point interpretation yields both sublinear and linear fixed-point residual convergence guarantees. For practical efficiency, cuPDQPx integrates diagonal preconditioning, step-size selection, adaptive restart, and adaptive primal and quadratic weight updates. cuPDQPx is implemented in C and CUDA with optimized sparse matrix-vector products, kernel fusion, and CUDA Graphs. Numerical experiments on the Maros-Mészáros collection, a convex subset of QPLIB, and synthetic large-scale QPs demonstrate that cuPDQPx has strong numerical performance at both 10−4 and 10−8 tolerances.
Related
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BibTeX
@misc{lu2026cupdqpx,
title = {{cuPDQPx: A GPU-Accelerated Restarted Halpern PDHG for Large-Scale Convex Quadratic Programming}},
author = {Haihao Lu and Zedong Peng and Jinwen Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38706},
eprint = {2610.38706},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38706},
}
RIS
TY - UNPB
TI - cuPDQPx: A GPU-Accelerated Restarted Halpern PDHG for Large-Scale Convex Quadratic Programming
AU - Haihao Lu
AU - Zedong Peng
AU - Jinwen Yang
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38706
UR - https://arxiv.org/abs/2610.38706
AB - We present cuPDQPx, a GPU-accelerated, factorization-free first-order solver for large-scale convex quadratic programming (QP). Building on the restarted reflected Halpern primal-dual framework of cuPDLPx, we introduce an auxiliary-variable splitting that yields explicit updates without linearizing the quadratic objective or solving inner quadratic subproblems. A preconditioned proximal point interpretation yields both sublinear and linear fixed-point residual convergence guarantees. For practical efficiency, cuPDQPx integrates diagonal preconditioning, step-size selection, adaptive restart, and adaptive primal and quadratic weight updates. cuPDQPx is implemented in C and CUDA with optimized sparse matrix-vector products, kernel fusion, and CUDA Graphs. Numerical experiments on the Maros-Mészáros collection, a convex subset of QPLIB, and synthetic large-scale QPs demonstrate that cuPDQPx has strong numerical performance at both 10^−4 and 10^−8 tolerances.
ER -