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

Please always quote using this URN:urn:nbn:de:0296-matheon-13504
  • 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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Metadaten
Author:Lars Lubkoll, Anton Schiela, Martin Weiser
URN:urn:nbn:de:0296-matheon-13504
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2015/12/23
Release Date:2015/12/23
Tag:affine covariant; composite step methods; cubic regularization; optimization with PDEs
Institute:Research Center Matheon
Zuse Institute Berlin (ZIB)
Project:A Life sciences / A-CH9 Adaptive algorithms for optimization of hip implant positioning
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M37 Methods of nonlinear programming type [See also 90C30, 65Kxx]
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C06 Large-scale problems
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C55 Methods of successive quadratic programming type
Preprint Number:1089
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