Smoothing Binary Optimization: A Primal-Dual Perspective
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913105373560832 |
|---|---|
| author | Liu, Wenbo Wang, Akang Ma, Dun Jiang, Hongyi Wu, Jianghua Yang, Wenguo |
| author_facet | Liu, Wenbo Wang, Akang Ma, Dun Jiang, Hongyi Wu, Jianghua Yang, Wenguo |
| contents | Binary optimization is a powerful tool for modeling combinatorial problems, yet scalable and theoretically sound solution methods remain elusive. Conventional solvers often rely on heuristic strategies with weak guarantees or struggle with large-scale instances. In this work, we introduce a novel primal-dual framework that reformulates unconstrained binary optimization as a continuous minimax problem, satisfying a strong max-min property. This reformulation effectively smooths the discrete problem, enabling the application of efficient gradient-based methods. We propose a simultaneous gradient descent-ascent algorithm that is highly parallelizable on GPUs and provably converges to a near-optimal solution in linear time. Extensive experiments on large-scale problems--including Max-Cut, MaxSAT, and Maximum Independent Set with up to 50,000 variables--demonstrate that our method identifies high-quality solutions within seconds, significantly outperforming state-of-the-art alternatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Smoothing Binary Optimization: A Primal-Dual Perspective Liu, Wenbo Wang, Akang Ma, Dun Jiang, Hongyi Wu, Jianghua Yang, Wenguo Optimization and Control Binary optimization is a powerful tool for modeling combinatorial problems, yet scalable and theoretically sound solution methods remain elusive. Conventional solvers often rely on heuristic strategies with weak guarantees or struggle with large-scale instances. In this work, we introduce a novel primal-dual framework that reformulates unconstrained binary optimization as a continuous minimax problem, satisfying a strong max-min property. This reformulation effectively smooths the discrete problem, enabling the application of efficient gradient-based methods. We propose a simultaneous gradient descent-ascent algorithm that is highly parallelizable on GPUs and provably converges to a near-optimal solution in linear time. Extensive experiments on large-scale problems--including Max-Cut, MaxSAT, and Maximum Independent Set with up to 50,000 variables--demonstrate that our method identifies high-quality solutions within seconds, significantly outperforming state-of-the-art alternatives. |
| title | Smoothing Binary Optimization: A Primal-Dual Perspective |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2509.21064 |