Gradient filter methods for predictive control with simple constraints

We present a framework for developing computationally efficient, first-order optimisation solvers using gradient filtering techniques. These solvers are similar in form to Nesterov´s fast gradient method, however they are differentiated by the increased number of historical iterations used in the gradient filter. The filter tap weights are selected offline by solving a system of algebraic equations such that bounds on the convergence rates of the filters are minimised. This approach was found to accelerate the convergence rate of the fast gradient method and could compute the solution of a test case quadratic programming problem, based on MPC of an atomic force microscope, in a shorter time than both the fast gradient and interior point methods.