On constraint qualifications in directionally differentiable multiobjective optimization problems
Giorgio Giorgi; Bienvenido Jiménez; Vincente Novo
RAIRO - Operations Research (2010)
- 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 38.3 (2010): 255-274. <http://eudml.org/doc/105314>.
@article{Giorgi2010,
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},
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},
month = {3},
number = {3},
pages = {255-274},
publisher = {EDP Sciences},
title = {On constraint qualifications in directionally differentiable multiobjective optimization problems},
url = {http://eudml.org/doc/105314},
volume = {38},
year = {2010},
}
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
DA - 2010/3//
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/105314
ER -
References
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- V. Novo and B. Jiménez, Lagrange multipliers in multiobjective optimization under mixed assumptions of Fréchet and directional differentiability, in 5th International Conference on Operations Research, University of La Habana, Cuba, March 4–8 (2002). Investigación Operacional25 (2004) 34–47.
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