← 研踪 PaperTrailarXiv:2610.38706 · v1
cuPDQPx: A GPU-Accelerated Restarted Halpern PDHG for Large-Scale Convex Quadratic Programming
首次提交 2026-10-29 03:05
版本更新 2026-10-29 03:05
雷达观测 2026-10-30 10:22
摘要
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.
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v1 · 2026-10-29 03:05 · 最新观测版本
cuPDQPx: A GPU-Accelerated Restarted Halpern PDHG for Large-Scale Convex Quadratic Programming
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.
查看此版本解读 →查看此版本原文 ↗