Cortild, Daniel (2023) Perturbed Inertial Krasnoselskii-Mann Iterations. Bachelor's Thesis, Mathematics.
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Abstract
Fixed point problems are essential to a lot of work in engineering and applied sciences nowadays. In this paper, we look into perturbed inertial Krasnoselskii-Mann iterations, building on the known-to-converge Krasnoselskii-Mann iterations and their inertial or perturbed versions. We consider a general inertial scheme, which includes both the heavy-ball method by Polyak and the momentum approach by Nesterov. The perturbations are added on each step and show the stability of the provided algorithm. We first establish weak convergence in the quasi-nonexpansive case and strong convergence in the quasi-contractive setting. We then lay out generalisations and examples, from which the real interest in these iterations surfaces. Finally, we explore the link between Krasnoselkii-Mann iterations and the solutions to minimisation problems, namely by the three-operator splitting method. We then illustrate this splitting scheme through an application to the image inpainting problem.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Peypouquet, J.G. and Bertoglio, C.A. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 05 Jun 2023 12:39 |
| Last Modified: | 05 Jun 2023 12:39 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/29721 |
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