Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations

Fredi Tröltzsch; Daniel Wachsmuth

ESAIM: Control, Optimisation and Calculus of Variations (2006)

  • Volume: 12, Issue: 1, page 93-119
  • ISSN: 1292-8119

Abstract

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In this paper sufficient optimality conditions are established for optimal control of both steady-state and instationary Navier-Stokes equations. The second-order condition requires coercivity of the Lagrange function on a suitable subspace together with first-order necessary conditions. It ensures local optimality of a reference function in a L s -neighborhood, whereby the underlying analysis allows to use weaker norms than L ∞ .

How to cite

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Tröltzsch, Fredi, and Wachsmuth, Daniel. "Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations." ESAIM: Control, Optimisation and Calculus of Variations 12.1 (2006): 93-119. <http://eudml.org/doc/244824>.

@article{Tröltzsch2006,
abstract = {In this paper sufficient optimality conditions are established for optimal control of both steady-state and instationary Navier-Stokes equations. The second-order condition requires coercivity of the Lagrange function on a suitable subspace together with first-order necessary conditions. It ensures local optimality of a reference function in a $L^s$-neighborhood, whereby the underlying analysis allows to use weaker norms than $L^\infty $.},
author = {Tröltzsch, Fredi, Wachsmuth, Daniel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {optimal control; Navier-Stokes equations; control constraints; second-order optimality conditions; first-order necessary conditions; second order optimality criterion},
language = {eng},
number = {1},
pages = {93-119},
publisher = {EDP-Sciences},
title = {Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations},
url = {http://eudml.org/doc/244824},
volume = {12},
year = {2006},
}

TY - JOUR
AU - Tröltzsch, Fredi
AU - Wachsmuth, Daniel
TI - Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2006
PB - EDP-Sciences
VL - 12
IS - 1
SP - 93
EP - 119
AB - In this paper sufficient optimality conditions are established for optimal control of both steady-state and instationary Navier-Stokes equations. The second-order condition requires coercivity of the Lagrange function on a suitable subspace together with first-order necessary conditions. It ensures local optimality of a reference function in a $L^s$-neighborhood, whereby the underlying analysis allows to use weaker norms than $L^\infty $.
LA - eng
KW - optimal control; Navier-Stokes equations; control constraints; second-order optimality conditions; first-order necessary conditions; second order optimality criterion
UR - http://eudml.org/doc/244824
ER -

References

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