- Primal-dual interior point methods for PDE-constrained optimization Michael Ulbrich (mulbrichma.tum.de) Stefan Ulbrich (ulbrichmathematik.tu-darmstadt.de) 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 $L^p$. It is shown that the developed primal-dual interior-point method converges globally and locally superlinearly. Not only the easier $L^\infty$-setting is analyzed, but also a more involved $L^q$-analysis, $q<\infty$, is presented. In $L^\infty$, the set of feasible controls contains interior points and the Fr\'echet differentiability of the perturbed optimality system can be shown. In the $L^q$-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 particular, two-norm techniques and a smoothing step are required. Keywords: interior point methods, PDE-constrained optimization, global convergence, superlinear local convergence, optimal control, infinite dimensional optimization Category 1: Nonlinear Optimization (Systems governed by Differential Equations Optimization ) Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization ) Category 3: Infinite Dimensional Optimization Citation: Technical Report, Fachbereich Mathematik, TU Darmstadt, Schlossgartenstr. 7, D-64289 Darmstadt, Germany and Zentrum Mathematik, TU Muenchen, Boltzmannstr. 3, D-85747 Garching, Germany, March 2006. Download: [Postscript][PDF]Entry Submitted: 04/24/2006Entry Accepted: 04/24/2006Entry Last Modified: 04/24/2006Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.