P. Giselsson, M.D. Doan, T. Keviczky, B. De Schutter, and A. Rantzer, "A distributed optimization algorithm with convergence rate O(1/k2) for distributed model predictive control," Tech. rep. 12-011, Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands, Mar. 2012. Submitted to a journal.
We propose a distributed optimization algorithm for mixed L1/L2-norm optimization based on accelerated gradient methods using dual decomposition. The algorithm achieves convergence rate O(1/k2), where k is the iteration number, which significantly improves the convergence rates of existing duality-based distributed optimization algorithms that achieve O(1/k). The performance of the developed algorithm is evaluated on randomly generated optimization problems arising in distributed Model Predictive Control (MPC). The evaluation shows that, when the problem data is sparse and large-scale, our algorithm outperforms state-of-the-art optimization software CPLEX and MOSEK.