The University of Southampton
University of Southampton Institutional Repository

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
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.
0095-4616
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).

Record type: Article

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.

Text
Veliov-Vuong2018_Article_GradientMethodsOnStronglyConve - Version of Record
Available under License Creative Commons Attribution.
Download (691kB)

More information

Accepted/In Press date: 1 April 2016
e-pub ahead of print date: 6 October 2018

Identifiers

Local EPrints ID: 434646
URI: http://eprints.soton.ac.uk/id/eprint/434646
ISSN: 0095-4616
PURE UUID: 4337f0b5-0a98-437b-8033-6e5184dbe4c5
ORCID for P. T. Vuong: ORCID iD orcid.org/0000-0002-1474-994X

Catalogue record

Date deposited: 04 Oct 2019 16:30
Last modified: 16 Mar 2024 04:42

Export record

Altmetrics

Contributors

Author: V. M. Veliov
Author: P. T. Vuong ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×