A line search improvement of efficient MPC

A recent lifting technique led to a computationally efficient Model Predictive Control (MPC) strategy in which the online optimization is performed using a univariate Newton-Raphson procedure. However this procedure solves a dual problem, preventing the use of warm starting or premature termination. By solving a primal problem, the current paper proposes a strategy that is more efficient than the Newton-Raphson method and enables warm starting and early termination. Extensive simulations show this to outperform the Newton-Raphson procedure and to have distinct advantages over alternative approaches based on quadratic programming or semidefinite programming.