Accelerated gradient methods and dual decomposition in distributed model predictive control

Reference:
P. Giselsson, M.D. Doan, T. Keviczky, B. De Schutter, and A. Rantzer, "Accelerated gradient methods and dual decomposition in distributed model predictive control," Automatica, vol. 49, no. 3, pp. 829-833, Mar. 2013.

Abstract:
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 (DMPC). The evaluation shows that, when the problem data is sparse and large-scale, our algorithm can outperform current state-of-the-art optimization software CPLEX and MOSEK.