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 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 $$0-1$$ 0 - 1 problem indicate that our proposed algorithm has advantage over the SDP methods.