We consider a multiobjective optimization problem with a feasible set defined by inequality and equality constraints such that all functions are, at least, Dini differentiable (in some cases, Hadamard differentiable and sometimes, quasiconvex). Several constraint qualifications are given in such a way that generalize both the qualifications introduced by Maeda and the classical ones, when the functions are differentiable. The relationships between them are analyzed. Finally, we give several Kuhn-Tucker type necessary conditions for a point to be Pareto minimum under the weaker constraint qualifications here proposed.
Mots clés : multiobjective optimization problems, constraint qualification, necessary conditions for Pareto minimum, Lagrange multipliers, tangent cone, Dini differentiable functions, Hadamard differentiable functions, quasiconvex functions
@article{RO_2004__38_3_255_0,
author = {Giorgi, Giorgio and Jim\'enez, Bienvenido and Novo, Vincente},
title = {On constraint qualifications in directionally differentiable multiobjective optimization problems},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {255--274},
publisher = {EDP-Sciences},
volume = {38},
number = {3},
year = {2004},
doi = {10.1051/ro:2004023},
mrnumber = {2091756},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro:2004023/}
}
TY - JOUR AU - Giorgi, Giorgio AU - Jiménez, Bienvenido AU - Novo, Vincente TI - On constraint qualifications in directionally differentiable multiobjective optimization problems JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2004 SP - 255 EP - 274 VL - 38 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro:2004023/ DO - 10.1051/ro:2004023 LA - en ID - RO_2004__38_3_255_0 ER -
%0 Journal Article %A Giorgi, Giorgio %A Jiménez, Bienvenido %A Novo, Vincente %T On constraint qualifications in directionally differentiable multiobjective optimization problems %J RAIRO - Operations Research - Recherche Opérationnelle %D 2004 %P 255-274 %V 38 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro:2004023/ %R 10.1051/ro:2004023 %G en %F RO_2004__38_3_255_0
Giorgi, Giorgio; Jiménez, Bienvenido; Novo, Vincente. On constraint qualifications in directionally differentiable multiobjective optimization problems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 38 (2004) no. 3, pp. 255-274. doi : 10.1051/ro:2004023. http://www.numdam.org/articles/10.1051/ro:2004023/
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