A method solves a quadratic programming (QP) problem in real-time implementations of model predictive control for automation applications. The method can be implemented for fine-grained parallel solutions. Due to the extreme simplicity of the method, even serial implementations offer considerable speed advantages. The method solves the problem by formulating, over a predetermined time interval, an optimization problem with a quadratic cost function, and linear state and control constraints as a quadratic program for the application. Then, the quadratic program is solved by applying a parallel quadratic programming update law starting from a positive initial estimate to obtain control actions for the application.