Implementable fast augmented Lagrangian optimization algorithm with application in embedded MPC

In this paper we present an adaptive variant of a fast augmented Lagrangian method for solving linearly constrained convex optimization problems arising e.g. in model predictive control for embedded linear systems. Mainly, our method relies on the combination of the excessive-gap-like smoothing technique and the inexact oracle framework, which have been presented in details in [13]. We briefly present the total computational complexity results, in particular we derive an overall computational complexity of order O (1 over ε) projections onto a primal set in order to obtain an ε-optimal solution for our original problem. Moreover, our adaptive variant of fast augmented Lagrangian method is implementable, i.e. it is based on computable stopping criteria and with computational complexity certificates. This makes it suitable for applications to embedded control where we need tight estimates on the computational complexity of the corresponding numerical algorithm.