Exact Complexity Certification of an Early-Terminating Standard Primal Active-Set Method for Quadratic Programming

Abstract

In this paper we present a method to exactly certify the iteration complexity of a primal active-set algorithm for quadratic programs which is terminated early, given a specific multi-parametric quadratic program. The primal active-set algorithm’s real-time applicability is, hence, improved by early termination, increasing its computational efficiency, and by the proposed certification method, providing guarantees on worst-case behaviour. The certification method is illustrated on a multi-parametric quadratic program originating from model predictive control of an inverted pendulum, for which the relationship between allowed suboptimality and iterations needed by the primal active-set algorithm is presented.