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arXiv · 2602.23967

PDHCG-II: An Enhanced Version of PDHCG for Large-Scale Convex QP

Hongpei Li·Yicheng Huang·Huikang Liu·Dongdong Ge·Yinyu Ye
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Abstract

Quadratic programming (QP) is a fundamental optimization model with wide-ranging applications in decision-making and machine learning, yet efficiently solving large-scale instances remains a major computational challenge. Building upon the recently developed PDHCG framework, we propose PDHCG-II, an enhanced first-order solver tailored for large-scale convex QPs. The proposed method explicitly exploits the quadratic structure of the objective and incorporates several key algorithmic innovations, including Halpern-type acceleration and a PID-controlled adaptive update of the primal-dual weight. To further improve practical performance, PDHCG-II introduces a refined adaptive termination criterion for inner subproblems to prevent over-solving, together with an infeasibility detection mechanism for robust handling of ill-posed instances. Extensive numerical experiments demonstrate that PDHCG-II consistently achieves 2.5-5 times speedups over PDHCG on standard QP benchmarks. To facilitate reproducibility and broader adoption, we release a CUDA-C implementation of PDHCG-II as open-source software.

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Hongpei Li, Yicheng Huang, Huikang Liu, Dongdong Ge, Yinyu Ye. 2026-02-27. PDHCG-II: An Enhanced Version of PDHCG for Large-Scale Convex QP. https://arxiv.org/abs/2602.23967

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