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

TL;DR

PDHCG-II is an improved first-order solver for large-scale convex quadratic programming that leverages problem structure and advanced algorithmic techniques to significantly accelerate computation.

Contribution

It introduces PDHCG-II, a novel enhanced solver with acceleration, adaptive updates, and robustness features, improving efficiency over previous methods for large-scale convex QPs.

Findings

Achieves 2.5-5 times speedup over PDHCG.

Effectively handles ill-posed instances with new detection mechanisms.

Provides open-source CUDA-C implementation for reproducibility.

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.