Abstract: 

In this talk, we aim to introduce an HPR-LP solver, an implementation of a Halpern Peaceman-Rachford (HPR) method with semi-proximal terms for solving linear programming (LP).  We start with showing that the HPR method enjoys the highly desired iteration complexity of O(1/k) in terms of the Karush-Kuhn-Tucker residual and the objective error via the theory developed recently for accelerated degenerate proximal point methods. Based on the complexity results, we then design an adaptive strategy of restart and penalty parameter update to improve the efficiency and robustness of the HPR method. We conduct extensive numerical experiments on different LP benchmark datasets using NVIDIA A100-SXM4-80GB GPU in different stopping tolerances. Our solver's Julia version achieves a 2.39x to 5.70x speedup measured by SGM10 on benchmark datasets with presolve (2.03x to 4.06x without presolve) over the award-winning solver PDLP with the tolerance of 10^{-8}. Several practical techniques underlining the efficiency of the HPR-LP solver will be highlighted.   

Biography：

Professor Defeng Sun is currently Chair Professor of Applied Optimization and Operations Research at the Hong Kong Polytechnic University and the President of the Hong Kong Mathematical Society.  He mainly publishes in non-convex continuous optimization and machine learning. Together with Professor Kim-Chuan Toh and Dr Liuqin Yang, he was awarded the triennial 2018 Beale--Orchard-Hays Prize for Excellence in Computational Mathematical Programming by the Mathematical Optimization Society. He served as editor-in-chief of Asia-Pacific Journal of Operational Research from 2011 to 2013 and he now serves as associate editor of Mathematical Programming, SIAM Journal on Optimization, Journal of Optimization Theory and Applications, Journal of the Operations Research Society of China, Journal of Computational Mathematics, and Science China: Mathematics. In 2020, he was elected as a Fellow of the societies CSIAM and SIAM and in 2021 he has received the Distinguished Collaborator Award from both the Hong Kong Research Center and Huawei Noah's Ark Lab for the contributions on developing efficient and robust techniques for solving huge scale linear programming models arising from production planning and supply chain logistics.  In 2022, he received the RGC Senior Research Fellow Scheme award. In 2024, he was elected as a Fellow of Operations Research Society of China.