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Superiorization and bounded perturbation resilience of a gradient projection algorithm solving the convex minimization problem

Superiorization and bounded perturbation resilience of a gradient projection algorithm solving... In this article, we use the superiorization methodology to investigate the bounded perturbations resilience of the gradient projection algorithm proposed in Ertürk et al. (J Nonlinear Convex Anal 21(4):943–951, 2020) for solving the convex minimization problem in Hilbert space setting. We obtain that the perturbed version of this gradient projection algorithm converges weakly to a solution of the convex minimization problem just like itself. We support our conclusion with an example in an infinitely dimensional Hilbert space. We also show that the superiorization methodology can be applied to the split feasibility and the inverse linear problems with the help of the perturbed gradient projection algorithm. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Optimization Letters Springer Journals

Superiorization and bounded perturbation resilience of a gradient projection algorithm solving the convex minimization problem

Ertürk, Müzeyyen; Salkım, Ahmet
Optimization Letters , Volume 17 (8) – Nov 1, 2023
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References (38)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
1862-4472
eISSN
1862-4480
DOI
10.1007/s11590-022-01961-y
Publisher site
See Article on Publisher Site

Abstract

In this article, we use the superiorization methodology to investigate the bounded perturbations resilience of the gradient projection algorithm proposed in Ertürk et al. (J Nonlinear Convex Anal 21(4):943–951, 2020) for solving the convex minimization problem in Hilbert space setting. We obtain that the perturbed version of this gradient projection algorithm converges weakly to a solution of the convex minimization problem just like itself. We support our conclusion with an example in an infinitely dimensional Hilbert space. We also show that the superiorization methodology can be applied to the split feasibility and the inverse linear problems with the help of the perturbed gradient projection algorithm.

Journal

Optimization Letters – Springer Journals

Published: Nov 1, 2023

Keywords: Bounded perturbation resilience; Superiorization; Gradient projection algorithm; Convex minimization problems; Linear inverse problems; Split feasibility problems

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