Complexity Certification of Proximal-Point Methods for Numerically Stable Quadratic Programming

When solving a quadratic program (QP), one can improve the numerical stability of any QP solver by performing proximal-point outer iterations, resulting in sequence better conditioned QPs. In this letter we present method which, for given multi-parametric (mpQP) and polyhedral set parameters, determines which sequences QPs will have to be solved when using iterations. By knowing sequence, bounds on worst-case complexity obtained, is importance in, example, real-time model predictive control (MPC) applications. Moreover, combine proposed with previous work certification active-set methods obtain more detailed method's complexity, namely total number inner