Combined partial conjugate gradient and gradient projection solver for MPC

The objective of this paper is to present fast algorithm for large scale box constrained quadratic program which arises from linear model predictive control (MPC) with hard limits on the inputs. The presented algorithm uses the combination of the gradient projection method and the partial conjugate gradient method. The special structure of the MPC problem is exploited so that the conjugate gradient method converges in a few number of iterations and the algorithm well suitable for processes with thousands of inputs and small number of outputs is obtained.