# HPR-QP: A dual Halpern Peaceman-Rachford method for solving large-scale convex composite quadratic programming

arXiv: https://arxiv.org/abs/2507.02470 · HTML: https://mlsanity.com/paper/2507.02470/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2025.

## Built on by (most cited first, 1 of 1)

- [Efficient and provably convergent end-to-end training of deep neural networks with linear constraints](https://mlsanity.com/paper/2605.11526/) (2026)

## Abstract (arXiv)

In this paper, we introduce HPR-QP, a dual Halpern Peaceman-Rachford (HPR) method designed for solving large-scale convex composite quadratic programming. One distinctive feature of HPR-QP is that, instead of working with the primal formulations, it builds on the novel restricted Wolfe dual introduced in recent years. It also leverages the symmetric Gauss-Seidel technique to simplify subproblem updates without introducing auxiliary slack variables that typically lead to slow convergence. By restricting updates to the range space of the Hessian of the quadratic objective function, HPR-QP employs proximal operators of smaller spectral norms to speed up the convergence. Shadow sequences are elaborately constructed to deal with the range space constraints. Additionally, HPR-QP incorporates adaptive restart and penalty parameter update strategies, derived from the HPR method's O(1/k) convergence in terms of the Karush-Kuhn-Tucker residual, to further enhance its performance and robustness. Extensive numerical experiments on benchmark data sets using a GPU demonstrate that our Julia implementation of HPR-QP significantly outperforms state-of-the-art solvers in both speed and scalability.