Automated Extension of Fixed Point PDE Solvers for Optimal Design with Bounded Retardation

Gauger, Nicolas, Griewank, Andreas, Hamdi, Adel, Kratzenstein, Claudia, Özkaya, Emre and Slawig, Thomas (2012) Automated Extension of Fixed Point PDE Solvers for Optimal Design with Bounded Retardation Constrained Optimization and Optimal Control for Partial Differential Equations. UNSPECIFIED, Basel, pp. 99-122. DOI https://doi.org/10.1007/978-3-0348-0133-1.

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Abstract

We study PDE-constrained optimization problems where the state equation is solved by a pseudo-time stepping or fixed point iteration. We present a technique that improves primal, dual feasibility and optimality simultaneously in each iteration step, thus coupling state and adjoint iteration and control/design update. Our goal is to obtain bounded retardation of this coupled iteration compared to the original one for the state, since the latter in many cases has only a Q-factor close to one. For this purpose and based on a doubly augmented Lagrangian, which can be shown to be an exact penalty function, we discuss in detail the choice of an appropriate control or design space preconditioner, discuss implementation issues and present a convergence analysis. We show numerical examples, among them applications from shape design in fluid mechanics and parameter optimization in a climate model.

Document Type: Book chapter
Keywords: Nonlinear optimization, fixed point solvers, exact penalty function, augmented Lagrangian, automatic Differentiation, aerodynamic shape optimization, parameter optimization, climate model
Research affiliation: OceanRep > The Future Ocean - Cluster of Excellence
Kiel University
DOI etc.: https://doi.org/10.1007/978-3-0348-0133-1
Date Deposited: 11 Sep 2019 13:08
Last Modified: 11 Sep 2019 13:08
URI: http://eprints.uni-kiel.de/id/eprint/47701

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