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A composite step method for equality constrained optimization on manifolds

Title data

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

Official URL: Volltext

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 in another language

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
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
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 09 Mar 2019 22:00
Last Modified: 23 Mar 2021 09:12
URI: https://eref.uni-bayreuth.de/id/eprint/47908