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A composite step method for equality constrained optimization on manifolds

URN to cite this document: urn:nbn:de:bvb:703-epub-4258-4

Title data

Ortiz, Julián ; Schiela, Anton:
A composite step method for equality constrained optimization on manifolds.
Bayreuth , 2019 . - 27 S.

Format:	PDF
Name:	CSM-manifold-paper.pdf
Version:	Preprint
Available under License	German copyright law. This contribution is freely accessible with the consent of the copyright holder on the basis of an (DFG-funded) alliance or national license. The document may be used free of charge for personal use. In addition, the reproduction, editing, distribution and any kind of exploitation require the written consent of the respective rights holder.

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Project information

Project title:	Project's official title Project's id Optimierung auf Mannigfaltigkeiten für die numerische Lösung von gleichungsbeschränkten Variationsproblemen SCHI 1379/3-1
Project financing:	Deutsche Forschungsgemeinschaft

Abstract

We present a composite step method, designed for equality constrained optimization on differentiable manifolds. The use of retractions allows us to pullback the involved mappings to linear spaces and use tools such as cubic regularization of the objective function and affine covariant damped Newton method for feasibility. We show fast local convergence when different chart retractions are considered. We test our method on equilibrium problems in finite elasticity where the stable equilibrium position of an inextensible transversely isotropic elastic rod under dead load is searched.

Further data

Item Type:	Preprint, postprint
Keywords:	composite step methods; retractions; optimization on manifolds
Subject classification:	49M37; 90C55; 90C06
DDC Subjects:	500 Science > 510 Mathematics
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics > Chair Applied Mathematics - Univ.-Prof. Dr. Anton Schiela Profile Fields > Advanced Fields > Nonlinear Dynamics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Profile Fields Profile Fields > Advanced Fields
Language:	English
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-epub-4258-4
Date Deposited:	04 Mar 2019 09:38
Last Modified:	18 Dec 2020 10:41
URI:	https://epub.uni-bayreuth.de/id/eprint/4258

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