Citation
Yingxin Zhou, Stefano Cipolla, and Phan T. Vuong, “A Barrier Primal Dual Hybrid Gradient Method for Solving Linear Programming Problems,” arXiv preprint arXiv:2608.26667, 2026.
Abstract
Zhou et al. introduce Barrier PDHG (BPDHG), which adds a logarithmic barrier to the PDHG framework for linear programming. The barrier replaces projection onto the nonnegative orthant with a closed-form proximal update that keeps primal iterates strictly positive. The resulting Barrier PDLP (BPDLP) method combines fixed-barrier BPDHG iterations with adaptive restarts, barrier-parameter updates, and warm starts between barrier stages. As the barrier parameter decreases, the perturbed KKT system approaches the KKT system of the original linear program.