# 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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- B. Jiménez and V. Novo, Alternative theorems and necessary optimality conditions for directionally differentiable multiobjective programs. J. Convex Anal.9 (2002) 97–116.
- B. Jiménez and V. Novo, Optimality conditions in directionally differentiable Pareto problems with a set constraint via tangent cones. Numer. Funct. Anal. Optim.24 (2003) 557–574.
- T. Maeda, Constraint qualifications in multiobjective optimization problems: differentiable case. J. Optim. Theory Appl.80 (1994) 483–500.
- O.L. Mangasarian, Nonlinear programming. McGraw-Hill, New York (1969).
- 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.
- V. Preda and I. Chitescu, On constraint qualification in multiobjective optimization problems: semidifferentiable case. J. Optim. Theory Appl.100 (1999) 417–433.
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