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Recently, several authors have suggested the use of first order methods, suchas fast dual ascent and the alternating direction method of multipliers, forembedded model predictive control. The main reason is that they can beimplemented using simple arithmetic operations only. However, a knownlimitation of gradient-based methods is that they are sensitive toill-conditioning of the problem data. In this paper, we present a fast dualgradient method for which the sensitivity to ill-conditioning is greatlyreduced. This is achieved by approximating the negative dual function with aquadratic upper bound with different curvature in different directions in thealgorithm, as opposed to having the same curvature in all directions as instandard fast gradient methods. The main contribution of this paper is acharacterization of the set of matrices that can be used to form such aquadratic upper bound to the negative dual function. We also describe how tochoose a matrix from this set to get an improved approximation of the dualfunction, especially if it is ill-conditioned, compared to the approximationused in standard fast dual gradient methods. This can give a significantlyimproved performance as illustrated by a numerical evaluation on anill-conditioned AFTI-16 aircraft model.

Improving Fast Dual Ascent for MPC - Part II: The Embedded Case