Halpern Peaceman-Rachford (HPR) Acceleration Methods

See the implementation of the HPR method for solving linear programming [Kaihuang Chen, Defeng Sun, Yancheng Yuan, Guojun Zhang, and Xinyuan Zhao, “HPR-LP: An implementation of an HPR method for solving linear programming”, arXiv:2408.12179 (August 2024)] and the theoretical foundation of the HPR method [Defeng Sun, Yancheng Yuan, Guojun Zhang, and Xinyuan Zhao, “Accelerating preconditioned ADMM via degenerate proximal point mappings”, SIAM Journal on Optimization 35:2 (2025) 1165–1193]. For solving optimal transport problems, please refer to [Guojun Zhang, Zhexuan Gu, Yancheng Yuan, and Defeng Sun, “HOT: An Efficient Halpern Accelerating Algorithm for Optimal Transport Problems”, IEEE Transactions on Pattern Analysis and Machine Intelligence (2025), in print. arXiv:2408.00598 (August 2024)] and [Guojun Zhang, Yancheng Yuan, and Defeng Sun, “An Efficient HPR Algorithm for the Wasserstein Barycenter Problem with $ O ({Dim (P)}/\varepsilon) $ Computational Complexity”. arXiv:2211.14881 (2022).]