Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions

Christian Meyer

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 13, Issue: 4, page 750-775
  • ISSN: 1292-8119

Abstract

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We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffuse-gray conductive-radiative heat transfer. After stating first-order necessary conditions, second-order sufficient conditions are derived that account for strongly active sets. These conditions ensure local optimality in an Ls-neighborhood of a reference function whereby the underlying analysis allows to use weaker norms than L .

How to cite

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Meyer, Christian. "Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions." ESAIM: Control, Optimisation and Calculus of Variations 13.4 (2007): 750-775. <http://eudml.org/doc/249996>.

@article{Meyer2007,
abstract = { We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffuse-gray conductive-radiative heat transfer. After stating first-order necessary conditions, second-order sufficient conditions are derived that account for strongly active sets. These conditions ensure local optimality in an Ls-neighborhood of a reference function whereby the underlying analysis allows to use weaker norms than $L^\infty$. },
author = {Meyer, Christian},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Optimal control; semilinear elliptic equations; nonlocal interface conditions; second-order sufficient optimality conditions; optimal control; nonlocal interface conditions; second-order sufficient optimality conditions},
language = {eng},
month = {7},
number = {4},
pages = {750-775},
publisher = {EDP Sciences},
title = {Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions},
url = {http://eudml.org/doc/249996},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Meyer, Christian
TI - Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/7//
PB - EDP Sciences
VL - 13
IS - 4
SP - 750
EP - 775
AB - We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffuse-gray conductive-radiative heat transfer. After stating first-order necessary conditions, second-order sufficient conditions are derived that account for strongly active sets. These conditions ensure local optimality in an Ls-neighborhood of a reference function whereby the underlying analysis allows to use weaker norms than $L^\infty$.
LA - eng
KW - Optimal control; semilinear elliptic equations; nonlocal interface conditions; second-order sufficient optimality conditions; optimal control; nonlocal interface conditions; second-order sufficient optimality conditions
UR - http://eudml.org/doc/249996
ER -

References

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  9. H.-J. Rost, D. Siche, J. Dolle, W. Eiserbeck, T. Müller, D. Schulz, G. Wagner and J. Wollweber, Influence of different growth parameters and related conditions on 6H-SiC crystals grown by the modified Lely method. Mater. Sci. Eng. B61-62 (1999) 68–72.  
  10. T. Tiihonen, A nonlocal problem arising from heat radiation on non-convex surfaces. Eur. J. App. Math.8 (1997) 403–416.  Zbl0889.45013
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