Block Coordinate Descent Network Simplex Methods for Optimal Transport

Lingrui Li; Nobuo Yamashita

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arXiv · 2506.21231

Block Coordinate Descent Network Simplex Methods for Optimal Transport

Lingrui Li·Nobuo Yamashita

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Abstract

We propose the Block Coordinate Descent Network Simplex (BCDNS) method for solving large-scale discrete Optimal Transport (OT) problems. BCDNS integrates the Network Simplex (NS) algorithm with a block coordinate descent (BCD) strategy, decomposing the full problem into smaller subproblems per iteration and reusing basis variables to ensure feasibility. We prove that BCDNS terminates in a finite number of iterations with an exact optimal solution, and we characterize its per-iteration complexity as O(s N), where s is a user-defined parameter in (0,1) and N is the total number of variables. Numerical experiments demonstrate that BCDNS matches the classical NS method in solution accuracy, reduces memory footprint compared to the Sinkhorn algorithm, achieves speed-ups of up to tens of times over the classical NS method, and exhibits runtime comparable to a high-precision Sinkhorn implementation.

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BibTeX RIS

Lingrui Li, Nobuo Yamashita. 2025-06-26. Block Coordinate Descent Network Simplex Methods for Optimal Transport. https://arxiv.org/abs/2506.21231

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