# On constraint qualifications in directionally differentiable multiobjective optimization problems

Giorgio Giorgi; Bienvenido Jiménez; Vincente Novo

RAIRO - Operations Research - Recherche Opérationnelle (2004)

- Volume: 38, Issue: 3, page 255-274
- ISSN: 0399-0559

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topGiorgi, Giorgio, Jiménez, Bienvenido, and Novo, Vincente. "On constraint qualifications in directionally differentiable multiobjective optimization problems." RAIRO - Operations Research - Recherche Opérationnelle 38.3 (2004): 255-274. <http://eudml.org/doc/246032>.

@article{Giorgi2004,

abstract = {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.},

author = {Giorgi, Giorgio, Jiménez, Bienvenido, Novo, Vincente},

journal = {RAIRO - Operations Research - Recherche Opérationnelle},

keywords = {multiobjective optimization problems; constraint qualification; necessary conditions for Pareto minimum; Lagrange multipliers; tangent cone; Dini differentiable functions; Hadamard differentiable functions; quasiconvex functions; Multiobjective optimization problems, constraint qualification, necessary conditions for Pareto minimum, Lagrange multipliers, tangent cone, Dini differentiable functions, Hadamard differentiable functions, quasiconvex functions.},

language = {eng},

number = {3},

pages = {255-274},

publisher = {EDP-Sciences},

title = {On constraint qualifications in directionally differentiable multiobjective optimization problems},

url = {http://eudml.org/doc/246032},

volume = {38},

year = {2004},

}

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

PB - EDP-Sciences

VL - 38

IS - 3

SP - 255

EP - 274

AB - 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.

LA - eng

KW - multiobjective optimization problems; constraint qualification; necessary conditions for Pareto minimum; Lagrange multipliers; tangent cone; Dini differentiable functions; Hadamard differentiable functions; quasiconvex functions; Multiobjective optimization problems, constraint qualification, necessary conditions for Pareto minimum, Lagrange multipliers, tangent cone, Dini differentiable functions, Hadamard differentiable functions, quasiconvex functions.

UR - http://eudml.org/doc/246032

ER -

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