Exact Complexity Certification of a Nonnegative Least-Squares Method for Quadratic Programming

In this letter we propose a method to exactly certify the complexity of an active-set method which is based on reformulating strictly convex quadratic programs to nonnegative least-squares problems. The exact complexity of the method is determined by proving the correspondence between the method and a standard primal active-set method for quadratic programming applied to the dual of the quadratic program to be solved. Once this correspondence has been established, a complexity certification method which has already been established for the primal active-set method is used to also certify the complexity of the nonnegative least-squares method. The usefulness of the proposed method is illustrated on a multi-parametric quadratic program originating from model predictive control of an inverted pendulum.