PDHCG-II：一种针对大规模凸二次规划的增强型PDHCG
PDHCG-II: An Enhanced Version of PDHCG for Large-Scale Convex QP
AI总结：
PDHCG-II是一种针对大规模凸二次规划问题的增强型求解器，通过引入Halpern型加速和PID控制的自适应更新机制，提高了求解效率和鲁棒性。
摘要：
二次规划（QP）是一种基本的优化模型，在决策制定和机器学习中有广泛的应用，但高效地解决大规模实例仍然是一个主要的计算挑战。在最近开发的PDHCG框架基础上，我们提出了PDHCG-II，一种专门针对大规模凸QP的增强型一阶求解器。所提出的方法明确利用了目标函数的二次结构，并集成了几种关键的算法创新，包括Halpern型加速和PID控制的对偶权重自适应更新。为进一步提高实际性能，PDHCG-II引入了改进的自适应终止准则用于子问题，以防止过度求解，同时引入了不一致性检测机制以稳健地处理不规范实例。广泛的数值实验表明，PDHCG-II在标准QP基准上 consistently 实现了2.5至5倍的速度提升。为了促进可重复性和更广泛的应用，我们发布了PDHCG-II的CUDA-C实现作为开源软件。
英文摘要：
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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