Interior Point Methods in Function Space for State Constraints - Inexact Newton and Adaptivity
Please always quote using this URN: urn:nbn:de:0297-zib-11007
- We consider an interior point method in function space for PDE constrained optimal control problems with state constraints. Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error of each Newton step is controlled by adaptive grid refinement in the innermost loop. This allows to perform most of the required Newton steps on coarse grids, such that the overall computational time is dominated by the last few steps. For this purpose we propose an a-posteriori error estimator for a problem suited norm.
| Author: | Anton Schiela, Andreas Günther |
|---|---|
| Document Type: | ZIB-Report |
| Tag: | adaptivity; function space; interior point methods; state constraints |
| 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] / 49M05 Methods based on necessary conditions |
| 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C51 Interior-point methods | |
| Date of first Publication: | 2008/12/10 |
| Series (Serial Number): | ZIB-Report (09-01) |
| ISSN: | 1438-0064 |
| ZIB-Reportnumber: | 09-01 |
| Published in: | A rev. vers. appeared u. the title "An interior point algorithm with inexact step computation in function space for state constrained optimal control" in: Numerische Mathematik 119(2): 373-407(2011) |
