On constraint qualifications in directionally differentiable multiobjective optimization problems
RAIRO - Operations Research - Recherche Opérationnelle, Tome 38 (2004) no. 3, pp. 255-274.

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.

DOI : 10.1051/ro:2004023
Classification : 90C29, 90C46
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},
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     doi = {10.1051/ro:2004023},
     mrnumber = {2091756},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ro:2004023/}
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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://archive.numdam.org/articles/10.1051/ro:2004023/

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