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When Model Predictive Control (MPC) is used in real-time to control linearsystems, quadratic programs (QPs) need to be solved within a limited timeframe. Recently, several parametric methods have been proposed that certify thenumber of computations active-set QP solvers require to solve these QPs. Thesecertification methods, hence, ascertain that the optimization problem can besolved within the limited time frame. A shortcoming in these methods is,however, that they do not account for numerical errors that might occurinternally in the solvers, which ultimately might lead to optimistic complexitybounds if, for example, the solvers are implemented in single precision. Inthis paper we propose a general framework that can be incorporated in any ofthese certification methods to account for such numerical errors.

Lift, Partition, and Project: Parametric Complexity Certification of Active-Set QP Methods in the Presence of Numerical Errors