Rate of convergence analysis of a dual fast gradient method for general convex optimization

In this paper we analyze the iteration complexity of a dual fast gradient method for solving general constrained convex problems, that can arise e.g in embedded model predictive control (MPC). When it is difficult to project on the primal feasible set described by convex constraints, we use the Lagrangian relaxation to handle the complicated constraints and then, we apply a dual fast gradient algorithm for solving the corresponding dual problem. We provide sublinear estimates on the primal suboptimality and feasibility violation of the generated approximate primal solutions. The iteration complexity analysis is based on two types of approximate primal solutions: the last primal iterate sequence and an average primal sequence. We also test the performance of the algorithm on MPC for a simplified model of a self balancing robot.