Inexact gradient projection method with relative error tolerance

TL;DR

This paper introduces an inexact gradient projection method that uses relative error tolerance for projections, providing convergence analysis and demonstrating advantages over exact projections in medium-scale least squares problems.

Contribution

It proposes a novel gradient projection algorithm with inexact projections based on relative error, along with convergence proofs and complexity bounds.

Findings

Convergence is established for the proposed method.

Numerical results show efficiency gains with inexact projections.

Method performs well on medium-scale least squares problems.

Abstract

A gradient projection method with feasible inexact projections is proposed in the present paper. The inexact projection is performed using a relative error tolerance. Asymptotic convergence analysis and iteration-complexity bounds of the method employing constant and Armijo step sizes are presented. Numerical results are reported illustrating the potential advantages of considering inexact projections instead of exact ones in some medium scale instances of a least squares problem over the spectrohedron.