On the inexact scaled gradient projection method

TL;DR

This paper introduces an inexact scaled gradient projection method that allows for approximate projections and non-monotone line searches, maintaining similar convergence properties to traditional methods.

Contribution

It presents a novel inexact version of the scaled gradient projection method with relaxed accuracy requirements and analyzes its convergence and complexity.

Findings

Method retains convergence properties of exact algorithms.

Allows inexact projections with controlled error.

Maintains iteration complexity bounds.

Abstract

The purpose of this paper is to present an inexact version of the scaled gradient projection method on a convex set, which is inexact in two sense. First, an inexact projection on the feasible set is computed, allowing for an appropriate relative error tolerance. Second, an inexact non-monotone line search scheme is employed to compute a step size which defines the next iteration. It is shown that the proposed method has similar asymptotic convergence properties and iteration-complexity bounds as the usual scaled gradient projection method employing monotone line searches.