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Geometric dynamics of optimization

Gay-Balmaz, François and Holm, Darryl D. and Ratiu, Tudor S. (2013) Geometric dynamics of optimization. Communications in Mathematical Sciences, 11 (1). pp. 163-231. ISSN 1539-6746. https://resolver.caltech.edu/CaltechAUTHORS:20130213-085449317

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Abstract

This paper investigates a family of dynamical systems arising from an evolutionary re-interpretation of certain optimal control and optimization problems. We focus particularly on the application in image registration of the theory of metamorphosis. Metamorphosis is a means of tracking the optimal changes of shape that are necessary for registration of images with various types of data structures, without requiring that the transformations of shape be diffeomorphisms, but penalizing them if they are not. The possibilities of this approach arc just beginning to be developed. In particular, metamorphosis and its related variants in the geometric approach to control and optimization can be expected to produce many exciting opportunities for new applications and analysis in geometric dynamics.


Item Type:Article
Related URLs:
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http://www.intlpress.com/CMS/2013/issue11-1/PublisherUNSPECIFIED
ORCID:
AuthorORCID
Ratiu, Tudor S.0000-0003-1972-5768
Additional Information:© 2013 International Press. Received: June 20, 2011; accepted (in revised form): May 4, 2012. Communicated by Andrea Bertozzi. We are grateful to A. M. Bloch, M. Bruveris, P. Constantin, C. J. Cotter, D. C. P. Ellis, B. A. Khesin, J. E. Marsden, D. Meier, A. Trouvé, F.-X. Vialard, and L. Younes for many useful and pleasant conversations about these and related matters. We also thank the referees for their thoughtful and constructive suggestions, which definitely improved the paper. The work by DDH was partially supported by a Wolfson Award from the Royal Society of London and an Advanced Grant from the European Research Council. FGB acknowledges the partial support of Swiss National Science Foundation grants 200020-117511 and of a Swiss National Science Foundation Postdoctoral Fellowship. TSR acknowledges the partial support of Swiss National Science Foundation grants 200020-117511, 200020-126630, and by the government grant of the Russian Federation for support of research projects implemented by leading scientists, Lomonosov Moscow State University under the agreement No. 11.G34.31.0054.
Funders:
Funding AgencyGrant Number
Royal Society of London Wolfson AwardUNSPECIFIED
European Research Council Advanced GrantUNSPECIFIED
Swiss National Science Foundation200020-11751
Swiss National Science Postdoctoral Fellowship200020-12630
Russian Federation government grantUNSPECIFIED
Lomonosov Moscow State University11.G34.31.0054
Subject Keywords:Optimal control, optimization, geometric mechanics. symmetry
Issue or Number:1
Classification Code:AMS subject classifications: 34H05, 49J20, 49J27
Record Number:CaltechAUTHORS:20130213-085449317
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130213-085449317
Official Citation:Geometric dynamics of optimization Francois Gay-Balmaz, Darryl D. Holm, and Tudor S. Ratiu p.163-231
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36892
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:13 Feb 2013 17:54
Last Modified:09 Mar 2020 13:19

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