We present GPU-accelerated Bregman Douglas–Rachford splitting algorithm (BDRS) for discrete optimal transport problem in three input formats: an explicit cost matrix, a point cloud with a ground cost between them, and a separable cost on a regular grid. For each input format, we propose hardware-aware designs of mathematically equivalent representations for the BDRS iterations to … Read more
Primal heuristics for finding high-quality feasible solutions are an important component in mixed-integer optimization (MIO) solvers. Recent advances in GPU-accelerated optimization algorithms show the potential of GPU acceleration for continuous optimization. In this paper, we introduce the Parallel Node Generation and Exploration Algorithm (PaNGEA), a GPU-friendly MIO primal heuristic. PaNGEA explores restricted subproblems by combining … Read more
We propose Log-Averaged Mirror Prox (LAMP), a linear-space primal-dual method for large-scale optimal transport. LAMP implements primal mirror prox updates by tracking an averaged dual sequence, reducing storage complexity from \({O}(nm)\) to \({O}(n+m)\) while preserving dense, GPU-friendly reductions. Consequently, LAMP preserves the last-iterate \(\widetilde{{O}}( nm\varepsilon^{-1})\) arithmetic complexity of conservatively parameterized primal-dual mirror prox. We further … Read more