  We propose a primal-dual interior-point (PDIP) method for solving quadratic
programming problems with linear inequality constraints that typically arise
form MPC applications. We show that the solver converges (locally)
quadratically to a suboptimal solution of the MPC problem. PDIP solvers rely on
two phases: the damped and the pure Newton phases. Compared to state-of-the-art
PDIP methods, our solver replaces the initial damped Newton phase (usually used
to compute a medium-accuracy solution) with a dual solver based on Nesterov's
fast gradient scheme (DFG) that converges with a sublinear convergence rate of
order O(1/k^2) to a medium-accuracy solution. The switching strategy to the
pure Newton phase, compared to the state of the art, is computed in the dual
space to exploit the dual information provided by the DFG in the first phase.
Removing the damped Newton phase has the additional advantage that our solver
saves the computational effort required by backtracking line search. The
effectiveness of the proposed solver is demonstrated on a 2-dimensional
discrete-time unstable system and on an aerospace application.
