A Newton-Based Dual Update Framework for ADMM in Convex Optimization Problems

The alternating-direction method of multipliers (ADMM) algorithm is a powerful tool for solving two-block structured convex optimization problems. This letter introduces a novel ADMM-based algorithm (Nwt-ADMM) that uses a Newton step to update the Lagrange multipliers of the two-block optimization problem. Conditions under which the method can be applied are investigated, together with the convergence properties in the case of consensus problems. Numerical tests have been conducted over regression problems to test the algorithm’s performances compared with state-of-the-art algorithms. The test demonstrates the superiority of the proposed algorithm in terms of the number of iterations needed and the run time to reach convergence.