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

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 tha...

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Vydané v:	Optimization letters Ročník 17; číslo 8; s. 1957 - 1978
Hlavní autori:	Ertürk, Müzeyyen, Salkım, Ahmet
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2023
Predmet:	Computational Intelligence Mathematics Mathematics and Statistics Numerical and Computational Physics Operations Research/Decision Theory Optimization Original Paper Simulation Gradient projection algorithm Bounded perturbation resilience Convex minimization problems Linear inverse problems Superiorization Split feasibility problems
ISSN:	1862-4472, 1862-4480
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Popis
Shrnutí:	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.
ISSN:	1862-4472 1862-4480
DOI:	10.1007/s11590-022-01961-y