An Entropy-Regularized ADMM For Binary Quadratic Programming

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...

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Bibliographic Details
Published in:Journal of global optimization Vol. 87; no. 2-4; pp. 447 - 479
Main Authors: Liu, Haoming, Deng, Kangkang, Liu, Haoyang, Wen, Zaiwen
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2023
Springer
Subjects:
Algorithms
Computer Science
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Alternating direction method of multipliers
Entropy penalty
Binary quadratic programming
Riemannian manifold
Low-rank factorization
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary: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.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01144-0