An affine covariant composite step method for optimization with PDEs as equality constraints

  • We propose a composite step method, designed for equality constrained optimization with partial differential equations. Focus is laid on the construction of a globalization scheme, which is based on cubic regularization of the objective and an affine covariant damped Newton method for feasibility. We show finite termination of the inner loop and fast local convergence of the algorithm. We discuss preconditioning strategies for the iterative solution of the arising linear systems with projected conjugate gradient. Numerical results are shown for optimal control problems subject to a nonlinear heat equation and subject to nonlinear elastic equations arising from an implant design problem in craniofacial surgery.
Metadaten
Author:Lars Lubkoll, Anton Schiela, Martin Weiser
Document Type:Article
Parent Title (English):Optimization Methods and Software
Volume:32
Issue:5
First Page:1132
Last Page:1161
Year of first publication:2017
Preprint:urn:nbn:de:0297-zib-53954
DOI:https://doi.org/10.1080/10556788.2016.1241783