A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems
Michael Hintermüller; Irwin Yousept
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 16, Issue: 3, page 503-522
- ISSN: 1292-8119
Access Full Article
top
Abstract
topHow to cite
topHintermüller, Michael, and Yousept, Irwin. "A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems." ESAIM: Control, Optimisation and Calculus of Variations 16.3 (2010): 503-522. <http://eudml.org/doc/250740>.
@article{Hintermüller2010,
abstract = {
Sensitivity analysis (with respect to the regularization parameter)
of the solution of a class of regularized state constrained
optimal control problems is performed. The theoretical results are
then used to establish an extrapolation-based numerical scheme for
solving the regularized problem for vanishing regularization
parameter. In this context, the extrapolation technique provides
excellent initializations along the sequence of reducing
regularization parameters. Finally, the favorable numerical
behavior of the new method is demonstrated and a comparison to
classical continuation methods is provided.
},
author = {Hintermüller, Michael, Yousept, Irwin},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Extrapolation; mixed control-state constraints; PDE-constrained optimization;
semismooth Newton algorithm; sensitivity; state constraints; extrapolation; semismooth Newton algorithm},
language = {eng},
month = {7},
number = {3},
pages = {503-522},
publisher = {EDP Sciences},
title = {A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems},
url = {http://eudml.org/doc/250740},
volume = {16},
year = {2010},
}
TY - JOUR
AU - Hintermüller, Michael
AU - Yousept, Irwin
TI - A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/7//
PB - EDP Sciences
VL - 16
IS - 3
SP - 503
EP - 522
AB -
Sensitivity analysis (with respect to the regularization parameter)
of the solution of a class of regularized state constrained
optimal control problems is performed. The theoretical results are
then used to establish an extrapolation-based numerical scheme for
solving the regularized problem for vanishing regularization
parameter. In this context, the extrapolation technique provides
excellent initializations along the sequence of reducing
regularization parameters. Finally, the favorable numerical
behavior of the new method is demonstrated and a comparison to
classical continuation methods is provided.
LA - eng
KW - Extrapolation; mixed control-state constraints; PDE-constrained optimization;
semismooth Newton algorithm; sensitivity; state constraints; extrapolation; semismooth Newton algorithm
UR - http://eudml.org/doc/250740
ER -
References
top- J.-J. Alibert and J.-P. Raymond, Boundary control of semilinear elliptic equations with discontinuous leading coefficients and unbounded controls. Numer. Funct. Anal. Optim.3/4 (1997) 235–250.
- E. Casas, Control of an elliptic problem with pointwise state contraints. SIAM J. Contr. Opt.4 (1986) 1309–1322.
- P. Deuflhard, Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms, Springer Series in Computational Mathematics35. Springer-Verlag, Berlin (2004).
- M. Hintermüller, Mesh-independence and fast local convergence of a primal-dual activ e–set method for mixed control-state constrained elliptic control problems. ANZIAM Journal49 (2007) 1–38.
- M. Hintermüller, K. Ito and K. Kunisch, The primal-dual active set strategy as a semismooth Newton method. SIAM J. Optim.13 (2003) 865–888.
- M. Hintermüller and K. Kunisch, Feasible and non-interior path-following in constrained minimization with low multiplier regularity. SIAM J. Control Optim.45 (2006) 1198–1221.
- M. Hintermüller and K. Kunisch, Path-following methods for a class of constrained minimization problems in function space. SIAM J. Optim.17 (2006) 159–187.
- M. Hintermüller, F. Tröltzsch and I. Yousept, Mesh-independence of semismooth Newton methods for Lavrentiev-regularized state constrained nonlinear optimal control problems. Numer. Math.108 (2008) 571–603.
- M. Hinze and C. Meyer, Variational discretization of Lavrentiev-regularized state constrained elliptic optimal control problems. Computat. Optim. Appl. (2009), doi: . DOI10.1007/s10589-008-9198-1
- C. Meyer, A. Rösch and F. Tröltzsch, Optimal control of PDEs with regularized pointwise state constraints. Comp. Optim. Appl.33 (2006) 209–228.
- C. Meyer, U. Prüfert and F. Tröltzsch, On two numerical methods for stat e–constrained elliptic control problems. Optim. Method. Softw.22 (2007) 871–899.
- F. Tröltzsch, Regular Lagrange multipliers for control problems with mixed pointwise control-state constraints. SIAM J. Optim.15 (2004/2005) 616–634 (electronic).
- F. Tröltzsch and I. Yousept, A regularization method for the numerical solution of elliptic boundary control problems with pointwise state constraints. Comp. Optim. Control42 (2009) 43–63.
- I. Yousept, Vergleich von Lösungsverfahren zur Behandlung elliptischer Optimalsteuerungsprobleme. Master's thesis, TU-Berlin, Germany (2005).
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.