Simple and Certifiable Quadratic Programming Algorithms for Embedded Linear Model Predictive Control

In this paper we review a dual fast gradient-projection approach to solving quadratic programming (QP) problems recently proposed in [Patrinos and Bemporad, 2012] that is particularly useful for embedded model predictive control (MPC) of linear systems subject to linear constraints on inputs and states. We show that the method has a computational effort aligned with several other existing QP solvers typically used in MPC, and in addition it is extremely easy to code, requires only basic and easily parallelizable arithmetic operations, and a number of iterations to reach a given accuracy in terms of optimality and feasibility of the primal solution that can be estimated quite tightly by solving an off-line mixed-integer linear programming problem.