Convergence Analysis of Consensus-ADMM for General QCQP

In this letter, we analyze the convergence properties of the consensus-alternating direction method of multipliers (ADMM) for solving general quadratically constrained quadratic programs. We prove that the consensus-ADMM converges under a mild condition, namely, the augmented Lagrangian parameter is chosen to be sufficiently large. It is shown that the augmented Lagrangian function is monotonically non-increasing under such a condition, and is bounded from below. Furthermore, we additionally prove the convergence of the point sequence generated by the consensus-ADMM. Numerical simulations confirm our theoretical analyses.