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

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CSM-manifold-paper.pdf - Preprint
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Project information

Project title:
Project's official titleProject's id
Optimierung auf Mannigfaltigkeiten für die numerische Lösung von gleichungsbeschränkten VariationsproblemenSCHI 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: 14 Mar 2019 13:23
URI: https://epub.uni-bayreuth.de/id/eprint/4258

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