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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Bibliographic Details
Published in:Optimization letters Vol. 17; no. 8; pp. 1957 - 1978
Main Authors: Ertürk, Müzeyyen, Salkım, Ahmet
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2023
Subjects:
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
Online Access:Get full text
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Summary: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