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Gradient Methods on Strongly Convex Feasible Sets and Optimal Control of Affine Systems
The paper presents new results about convergence of the gradient projection and the conditional gradient methods for abstract minimization problems on strongly convex sets. In particular, linear convergence is proved, although the objective functional does not need to be convex. Such problems arise,...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer US
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7319312/ https://www.ncbi.nlm.nih.gov/pubmed/32624632 http://dx.doi.org/10.1007/s00245-018-9528-3 |
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author | Veliov, V. M. Vuong, P. T. |
author_facet | Veliov, V. M. Vuong, P. T. |
author_sort | Veliov, V. M. |
collection | PubMed |
description | The paper presents new results about convergence of the gradient projection and the conditional gradient methods for abstract minimization problems on strongly convex sets. In particular, linear convergence is proved, although the objective functional does not need to be convex. Such problems arise, in particular, when a recently developed discretization technique is applied to optimal control problems which are affine with respect to the control. This discretization technique has the advantage to provide higher accuracy of discretization (compared with the known discretization schemes) and involves strongly convex constraints and possibly non-convex objective functional. The applicability of the abstract results is proved in the case of linear-quadratic affine optimal control problems. A numerical example is given, confirming the theoretical findings. |
format | Online Article Text |
id | pubmed-7319312 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
spelling | pubmed-73193122020-07-01 Gradient Methods on Strongly Convex Feasible Sets and Optimal Control of Affine Systems Veliov, V. M. Vuong, P. T. Appl Math Optim Article The paper presents new results about convergence of the gradient projection and the conditional gradient methods for abstract minimization problems on strongly convex sets. In particular, linear convergence is proved, although the objective functional does not need to be convex. Such problems arise, in particular, when a recently developed discretization technique is applied to optimal control problems which are affine with respect to the control. This discretization technique has the advantage to provide higher accuracy of discretization (compared with the known discretization schemes) and involves strongly convex constraints and possibly non-convex objective functional. The applicability of the abstract results is proved in the case of linear-quadratic affine optimal control problems. A numerical example is given, confirming the theoretical findings. Springer US 2018-10-06 2020 /pmc/articles/PMC7319312/ /pubmed/32624632 http://dx.doi.org/10.1007/s00245-018-9528-3 Text en © The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Article Veliov, V. M. Vuong, P. T. Gradient Methods on Strongly Convex Feasible Sets and Optimal Control of Affine Systems |
title | Gradient Methods on Strongly Convex Feasible Sets and Optimal Control of Affine Systems |
title_full | Gradient Methods on Strongly Convex Feasible Sets and Optimal Control of Affine Systems |
title_fullStr | Gradient Methods on Strongly Convex Feasible Sets and Optimal Control of Affine Systems |
title_full_unstemmed | Gradient Methods on Strongly Convex Feasible Sets and Optimal Control of Affine Systems |
title_short | Gradient Methods on Strongly Convex Feasible Sets and Optimal Control of Affine Systems |
title_sort | gradient methods on strongly convex feasible sets and optimal control of affine systems |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7319312/ https://www.ncbi.nlm.nih.gov/pubmed/32624632 http://dx.doi.org/10.1007/s00245-018-9528-3 |
work_keys_str_mv | AT veliovvm gradientmethodsonstronglyconvexfeasiblesetsandoptimalcontrolofaffinesystems AT vuongpt gradientmethodsonstronglyconvexfeasiblesetsandoptimalcontrolofaffinesystems |