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Primal-dual interior-point methods for PDE-constrained optimization.
- Source :
- Mathematical Programming; Mar2009, Vol. 117 Issue 1/2, p435-485, 51p, 2 Charts, 1 Graph
- Publication Year :
- 2009
-
Abstract
- This paper provides a detailed analysis of a primal-dual interior-point method for PDE-constrained optimization. Considered are optimal control problems with control constraints in L <superscript> p </superscript>. It is shown that the developed primal-dual interior-point method converges globally and locally superlinearly. Not only the easier L <superscript>∞</superscript>-setting is analyzed, but also a more involved L <superscript> q </superscript>-analysis, q < ∞, is presented. In L <superscript>∞</superscript>, the set of feasible controls contains interior points and the Fréchet differentiability of the perturbed optimality system can be shown. In the L <superscript> q </superscript>-setting, which is highly relevant for PDE-constrained optimization, these nice properties are no longer available. Nevertheless, a convergence analysis is developed using refined techniques. In parti- cular, two-norm techniques and a smoothing step are required. The L <superscript> q </superscript>-analysis with smoothing step yields global linear and local superlinear convergence, whereas the L <superscript>∞</superscript>-analysis without smoothing step yields only global linear convergence. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00255610
- Volume :
- 117
- Issue :
- 1/2
- Database :
- Complementary Index
- Journal :
- Mathematical Programming
- Publication Type :
- Academic Journal
- Accession number :
- 32961000
- Full Text :
- https://doi.org/10.1007/s10107-007-0168-7