Gradient methods on strongly convex feasible sets and optimal control of affine systems
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, 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.
Veliov, V. M.
69723e2e-1b2c-49e8-bf58-89b68ef17cc1
Vuong, P. T.
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Veliov, V. M.
69723e2e-1b2c-49e8-bf58-89b68ef17cc1
Vuong, P. T.
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Veliov, V. M. and Vuong, P. T.
(2018)
Gradient methods on strongly convex feasible sets and optimal control of affine systems.
Applied Mathematics & Optimization.
(doi:10.1007/s00245-018-9528-3).
Abstract
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.
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Veliov-Vuong2018_Article_GradientMethodsOnStronglyConve
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Accepted/In Press date: 1 April 2016
e-pub ahead of print date: 6 October 2018
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Local EPrints ID: 434646
URI: http://eprints.soton.ac.uk/id/eprint/434646
ISSN: 0095-4616
PURE UUID: 4337f0b5-0a98-437b-8033-6e5184dbe4c5
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Date deposited: 04 Oct 2019 16:30
Last modified: 16 Mar 2024 04:42
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Author:
V. M. Veliov
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