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

Please always quote using this URN: urn:nbn:de:0297-zib-53954
  • 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.

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Author:Lars Lubkoll, Anton Schiela, Martin Weiser
Document Type:ZIB-Report
Tag:affine covariant; composite step methods; cubic regularization; optimization with PDEs
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]
Date of first Publication:2015/03/12
Series (Serial Number):ZIB-Report (15-09)
Published in:Optimization Methods and Software, DOI 10.1080/10556788.2016.1241783

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