Preconditioning of conjugate gradient iterations in interior point MPC method

There are several efficient direct solvers for structured systems of linear equations defining search directions in primal-dual interior point methods applied to constrained model predictive control problems. We propose reusing matrix decompositions of direct solvers as preconditioners in Krylov-subspace methods applied to subsequent iterations of the interior point method, which results in at least halving its asymptotic computational complexity. We also analyze sensitivity of direct solvers to the regularization parameters.