Recent Developments in HPR Methods for Large-Scale Convex Composite Quadratic Programming
Abstract
We present recent developments in Halpern Peaceman--Rachford (HPR) methods for solving large-scale convex composite quadratic programming problems. Within a unified HPR framework applied to the restricted Wolfe dual, we develop several algorithmic variants based on different choices of the semi-proximal operator 𝒯1 for the joint dual subproblem. Specifically, an sGS-based construction leads to a sequential w--y--w update scheme, while a block-linearized construction eliminates cross-block coupling and enables parallel dual updates. To improve the latter, we further introduce a coupling-aware construction that exploits a second spectral moment to obtain a tighter row majorizer. We extend the framework to convex quadratically constrained quadratic programming through factor-based second-order cone reformulations. Additional computational enhancements include equality Gram scaling and asynchronous CPU polishing. We establish convergence results under fixed metrics and discuss practical adaptive strategies.
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BibTeX
@misc{chen2026recent,
title = {{Recent Developments in HPR Methods for Large-Scale Convex Composite Quadratic Programming}},
author = {Kaihuang Chen and Defeng Sun and Yancheng Yuan and Guojun Zhang and Xinyuan Zhao},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01887},
eprint = {2611.01887},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01887},
}
RIS
TY - UNPB
TI - Recent Developments in HPR Methods for Large-Scale Convex Composite Quadratic Programming
AU - Kaihuang Chen
AU - Defeng Sun
AU - Yancheng Yuan
AU - Guojun Zhang
AU - Xinyuan Zhao
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01887
UR - https://arxiv.org/abs/2611.01887
AB - We present recent developments in Halpern Peaceman--Rachford (HPR) methods for solving large-scale convex composite quadratic programming problems. Within a unified HPR framework applied to the restricted Wolfe dual, we develop several algorithmic variants based on different choices of the semi-proximal operator 𝒯_1 for the joint dual subproblem. Specifically, an sGS-based construction leads to a sequential w--y--w update scheme, while a block-linearized construction eliminates cross-block coupling and enables parallel dual updates. To improve the latter, we further introduce a coupling-aware construction that exploits a second spectral moment to obtain a tighter row majorizer. We extend the framework to convex quadratically constrained quadratic programming through factor-based second-order cone reformulations. Additional computational enhancements include equality Gram scaling and asynchronous CPU polishing. We establish convergence results under fixed metrics and discuss practical adaptive strategies.
ER -