A variant to Sequential Quadratic Programming for nonlinear Model Predictive Control

Sequential Quadratic Programming (SQP) denotes an established class of methods for solving nonlinear optimization problems via an iterative sequence of Quadratic Programs (QPs). Several approaches in the literature have established local and global convergence of the method. This paper considers a variant to SQP that, instead of solving each QP, at each iteration follows one gradient step along a direction that is proven to be a descent direction for an augmented Lagrangian of the nonlinear problem, and in turn is used to generate the next QP. We prove global convergence to a critical point of the original nonlinear problem via a line search that requires the same assumptions as the SQP method. The method is then applied to nonlinear Model Predictive Control (MPC). To simplify the problem formulation and achieve faster convergence, we propose a locally convergent reformulation. An important speed-up is observed in practice via a specific initialization. The computational efficiency of the proposed method is finally shown in a numerical example.