Huber, Johannes. Interior-point methods for PDE-constrained optimization. 2013, PhD Thesis, University of Basel, Faculty of Science.
Official URL: http://edoc.unibas.ch/diss/DissB_10439
In this thesis interior-point (IP) methods are considered to solve nonconvex large-scale PDE-constrained optimization problems with inequality constraints. To cope with enormous fill-in of direct linear solvers, inexact search directions are allowed in an inexact interior-point (IIP) method. This thesis builds upon the IIP method proposed in [Curtis, Schenk, Wächter, SIAM Journal on Scientific Computing, 2010]. SMART tests cope with the lack of inertia information to control Hessian modification and also specify termination tests for the iterative linear solver.
The original IIP method needs to solve two sparse large-scale linear systems in each optimization step. This is improved to only a single linear system solution in most optimization steps. Within this improved IIP framework, two iterative linear solvers are evaluated: A general purpose algebraic multilevel incomplete L D L^T preconditioned SQMR method is applied to PDE-constrained optimization problems for optimal server room cooling in three space dimensions and to compute an ambient temperature for optimal cooling. The results show robustness and efficiency of the IIP method when compared with the exact IP method.
These advantages are even more evident for a reduced-space preconditioned (RSP) GMRES solver which takes advantage of the linear system's structure. This RSP-IIP method is studied on the basis of distributed and boundary control problems originating from superconductivity and from two-dimensional and three-dimensional parameter estimation problems in groundwater modeling. The numerical results exhibit the improved efficiency especially for multiple PDE constraints.
An inverse medium problem for the Helmholtz equation with pointwise box constraints is solved by IP methods. The ill-posedness of the problem is explored numerically and different regularization strategies are compared. The impact of box constraints and the importance of Hessian modification on the optimization algorithm is demonstrated. A real world seismic imaging problem is solved successfully by the RSP-IIP method.
|Advisors:||Grote, Marcus J.|
|Committee Members:||Schenk, Olaf and Haber, Eldad|
|Faculties and Departments:||05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Numerik (Grote)|
|Bibsysno:||Link to catalogue|
|Number of Pages:||136 S.|
|Last Modified:||30 Jun 2016 10:53|
|Deposited On:||30 Jul 2013 10:14|
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