A computationally efficient primal–dual solver for linear-quadratic optimal control problems

This paper presents a fast projected primal–dual method for solving linear-quadratic optimal control problems. The computational efficiency comes from a heavy-ball acceleration and specific (sparse) choices of preconditioning matrices. To analyse convergence, we first assume that the weighing matrices in the linear quadratic optimal control problems are diagonal, allowing us to propose the preconditioning matrices and study the convergence of the resulting algorithm by writing it a Lur'e-type dynamic system. We then employ this preconditioned algorithm for the case that weighting matrices are nondiagonal by applying the preconditioned algorithm repeatedly in a sequential-quadratic programming fashion. Furthermore, it is shown that infeasibility of the optimal control problem can be detected using the Theorem of the Alternatives and the iterates produced by the algorithm. The resulting algorithm is simple, while also achieving competitive computational times.