Accelerating the Iteratively Preconditioned Gradient-Descent Algorithm using Momentum

Abstract

In this paper, we investigate the idea of employing the momentum technique in the iteratively preconditioned gradient-descent (IPG) algorithm with the aim of an improved performance than our previous results. Three formulations are proposed utilizing different momentum terms. A convergence proof is presented for each formulation, providing sufficient conditions for the parameter selections leading to a linear convergence rate. The proposed optimization approaches are applied in the moving horizon estimation (MHE) framework for a unicycle mobile robot location estimation example. The simulation results confirm that the total number of iterations can be reduced when introducing the momentum terms into the original IPG approach.