Inexact log-domain interior-point methods for quadratic programming

This paper introduces a framework for implementing log-domain interior-point methods (LDIPMs) using inexact Newton steps. A generalized inexact iteration scheme is established that is globally convergent and locally quadratically convergent towards centered points if the residual of the inexact Newton step satisfies a set of termination criteria. Three inexact LDIPM implementations based on the conjugate gradient (CG) method are developed using this framework. In a set of computational experiments, the inexact LDIPMs demonstrate a 24–72% reduction in the total number of CG iterations required for termination relative to implementations with a fixed termination tolerance. This translates into an important computation time reduction in applications such as real-time optimization and model predictive control.