Active-Set based Inexact Interior Point QP Solver for Model Predictive Control

Abstract

Interior point methods are applicable to a large class of problems and can be very reliable for convex optimization, even without a good initial guess for the optimal solution. Active-set methods, on the other hand, are often restricted to linear or quadratic programming but they have a lower computational cost per iteration and superior warm starting properties. The present paper proposes an approach for improving the numerical conditioning and warm starting properties of interior point methods, based on an active-set identification strategy and inexact Newton-type optimization techniques. In addition, we show how this reduces the average computational cost of the linear algebra operations in each interior point iteration. We developed an efficient C code implementation of the active-set based interior point method (ASIPM) and show that it can be competitive with state of the art solvers for a standard case study of model predictive control stabilizing an inverted pendulum on a cart.