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Towards Computational Complexity Certification for Constrained MPC Based on Lagrange Relaxation and the Fast Gradient Method


S. Richter

IEEE Conference on Decision and Control, Orlando, FL, USA

This paper discusses the certification of Nesterov's fast gradient method for problems with a strongly convex quadratic objective and a feasible set given as the intersection of a parametrized affine set and a convex set. For this, we derive a lower iteration bound for the solution of the dual problem that is obtained from a partial Lagrange Relaxation and propose a new constant step-size rule that we prove to be optimal under mild assumptions. Finally, we apply the certification procedure to a constrained MPC problem and show that the new step-size rule improves performance significantly.


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M. Morari

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