Saved in:
| Main Authors: | , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.08852 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912755780419584 |
|---|---|
| author | Salloum, Hadi Hildebrand, Roland Nguyen, Nhat Trung Pirau, Vitali Badr, Amer Al Alkousa, Mohammad Gasnikov, Alexander |
| author_facet | Salloum, Hadi Hildebrand, Roland Nguyen, Nhat Trung Pirau, Vitali Badr, Amer Al Alkousa, Mohammad Gasnikov, Alexander |
| contents | We present a novel approach to accelerate the Goemans-Williamson (GW) randomized rounding procedure for quadratic unconstrained binary optimization (QUBO) problems. Instead of solving the conventional semi-definite programming (SDP) relaxation, which is computationally expensive, we employ a difference-of-convex (DC) optimization framework to efficiently approximate the SDP solution. The DC optimization produces candidate vectors that are then used within the GW randomized rounding scheme to generate high-quality binary solutions. Furthermore, we perform direct expectation minimization over manifolds of matrices with limited rank to further enhance the solution quality. Our method is benchmarked on real-world QUBO instances, including inverse kinematics problems, and compared against state-of-the-art solvers, such as quantum-inspired algorithms, demonstrating competitive approximation guarantees alongside substantial computational gains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Speeding up the Goemans-Williamson randomized procedure by difference-of-convex optimization Salloum, Hadi Hildebrand, Roland Nguyen, Nhat Trung Pirau, Vitali Badr, Amer Al Alkousa, Mohammad Gasnikov, Alexander Optimization and Control 90C09, 90C27 We present a novel approach to accelerate the Goemans-Williamson (GW) randomized rounding procedure for quadratic unconstrained binary optimization (QUBO) problems. Instead of solving the conventional semi-definite programming (SDP) relaxation, which is computationally expensive, we employ a difference-of-convex (DC) optimization framework to efficiently approximate the SDP solution. The DC optimization produces candidate vectors that are then used within the GW randomized rounding scheme to generate high-quality binary solutions. Furthermore, we perform direct expectation minimization over manifolds of matrices with limited rank to further enhance the solution quality. Our method is benchmarked on real-world QUBO instances, including inverse kinematics problems, and compared against state-of-the-art solvers, such as quantum-inspired algorithms, demonstrating competitive approximation guarantees alongside substantial computational gains. |
| title | Speeding up the Goemans-Williamson randomized procedure by difference-of-convex optimization |
| topic | Optimization and Control 90C09, 90C27 |
| url | https://arxiv.org/abs/2512.08852 |