An ADMM based method for underdetermined box-constrained integer least squares problems

To solve underdetermined box-constrained integer least squares (UBILS) problems, we propose an integer-constrained alternating direction method of multipliers (IADMM), which can be much more accurate than the ADMM method. To guarantee to find the optimal solution, then we incorporate IADMM to DTS, a tree search method, to make the latter more efficient. Numerical tests show that the combined method IADMM-DTS can be much faster than the original DTS method. Finally, we apply the combined method to a practical communication problem. Numerical results indicate that IADMM-DTS typically performs better than the commercial solvers CPLEX and MOSEK in terms of both efficiency and accuracy, and it can be used as an alternative to the commercial solver Gurobi for UBILS problems.