Block Coordinate Descent Network Simplex Methods for Optimal Transport
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917188141580288 |
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| author | Li, Lingrui Yamashita, Nobuo |
| author_facet | Li, Lingrui Yamashita, Nobuo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21231 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Block Coordinate Descent Network Simplex Methods for Optimal Transport Li, Lingrui Yamashita, Nobuo Optimization and Control 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. |
| title | Block Coordinate Descent Network Simplex Methods for Optimal Transport |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2506.21231 |