A general framework for calculating shape derivatives for optimization problems with partial differential equations as constraints is presented. The proposed technique allows to obtain the shape derivative of the cost without the necessity to involve the shape derivative of the state variable. In fact, the state variable is only required to be Lipschitz continuous with respect to the geometry perturbations. Applications to inverse interface problems, and shape optimization for elliptic systems and the Navier-Stokes equations are given.
@article{COCV_2008__14_3_517_0,
author = {Peichl, Gunther H. and Kunisch, Karl and Ito, Kazufumi},
title = {Variational approach to shape derivatives},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {517--539},
publisher = {EDP-Sciences},
volume = {14},
number = {3},
year = {2008},
doi = {10.1051/cocv:2008002},
mrnumber = {2434064},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv:2008002/}
}
TY - JOUR AU - Peichl, Gunther H. AU - Kunisch, Karl AU - Ito, Kazufumi TI - Variational approach to shape derivatives JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 SP - 517 EP - 539 VL - 14 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2008002/ DO - 10.1051/cocv:2008002 LA - en ID - COCV_2008__14_3_517_0 ER -
%0 Journal Article %A Peichl, Gunther H. %A Kunisch, Karl %A Ito, Kazufumi %T Variational approach to shape derivatives %J ESAIM: Control, Optimisation and Calculus of Variations %D 2008 %P 517-539 %V 14 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2008002/ %R 10.1051/cocv:2008002 %G en %F COCV_2008__14_3_517_0
Peichl, Gunther H.; Kunisch, Karl; Ito, Kazufumi. Variational approach to shape derivatives. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 3, pp. 517-539. doi : 10.1051/cocv:2008002. http://archive.numdam.org/articles/10.1051/cocv:2008002/
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