PDHCG-II: An Enhanced Version of PDHCG for Large-Scale Convex QP
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918359973494784 |
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| author | Li, Hongpei Huang, Yicheng Liu, Huikang Ge, Dongdong Ye, Yinyu |
| author_facet | Li, Hongpei Huang, Yicheng Liu, Huikang Ge, Dongdong Ye, Yinyu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23967 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | PDHCG-II: An Enhanced Version of PDHCG for Large-Scale Convex QP Li, Hongpei Huang, Yicheng Liu, Huikang Ge, Dongdong Ye, Yinyu Optimization and Control 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. |
| title | PDHCG-II: An Enhanced Version of PDHCG for Large-Scale Convex QP |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2602.23967 |