Bounded perturbation resilience of projected scaled gradient methods

TL;DR

This paper analyzes the convergence of projected scaled gradient methods for convex optimization, demonstrating their resilience to bounded perturbations, which supports their application in the superiorization methodology and enhances algorithm robustness.

Contribution

It establishes convergence of PSG methods under bounded perturbations, broadening their applicability and linking them to the superiorization framework.

Findings

Proves convergence of PSG methods with bounded perturbations

Shows PSG methods include several classical algorithms as special cases

Supports the use of PSG in superiorization and EM algorithms

Abstract

We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection onto the constraint set. This constitutes a generalized algorithmic structure that encompasses as special cases the gradient projection method, the projected Newton method, the projected Landweber-type methods and the generalized Expectation-Maximization (EM)-type methods. We prove the convergence of the PSG methods in the presence of bounded perturbations. This resilience to bounded perturbations is relevant to the ability to apply the recently developed superiorization methodology to PSG methods, in particular to the EM algorithm.