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An Entropy-Regularized ADMM For Binary Quadratic Programming

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Abstract

We propose an entropy regularized splitting model using low-rank factorization for solving binary quadratic programming with linear inequality constraints. Different from the semidefinite programming relaxation model, our model preserves the rank-one constraint and aims to find high quality rank-one solutions directly. The factorization transforms the variables into low-rank matrices, while the entropy term enforces the low-rank property of the splitting variable . A customized alternating direction method of multipliers is utilized to solve the proposed model. Specifically, our method uses the augmented Lagrangian function to deal with inequality constraints, and solves one subproblem on the oblique manifold by a regularized Newton method. Numerical results on the multiple-input multiple-output detection problem, the maxcut problem and the quadratic \(0-1\) problem indicate that our proposed algorithm has advantage over the SDP methods.

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Acknowledgements

The authors are grateful to the AE and two anonymous referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. Bei**g International Center for Mathematical Research, Peking University, Bei**g, China

    Haoming Liu, Kangkang Deng & Haoyang Liu

  2. Bei**g International Center for Mathematical Research, Center for Data Science and College of Engineering, Peking University, Bei**g, China

    Zaiwen Wen

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Z. Wen was supported in part by the NSFC grant 11831002.

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Liu, H., Deng, K., Liu, H. et al. An Entropy-Regularized ADMM For Binary Quadratic Programming. J Glob Optim 87, 447–479 (2023). https://doi.org/10.1007/s10898-022-01144-0

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