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On constraint qualifications in directionally differentiablemultiobjective optimization problems

Published online by Cambridge University Press:  15 September 2004

Giorgio Giorgi ,
Bienvenido Jiménez  and
Vincente Novo
Giorgio Giorgi
Affiliation:
Dipartimento di Ricerche Aziendali, Università degli Studi di Pavia, Via S. Felice, 5, 27100 Pavia, Italy; ggiorgi@eco.unipv.it.
Bienvenido Jiménez
Affiliation:
Departamento de Economía e Historia Económica, Facultad de Economía y Empresa, Universidad de Salamanca, Campus Miguel de Unamuno, s/n, 37007 Salamanca, Spain; bjimen1@encina.pntic.mec.es.
Vincente Novo
Affiliation:
Departamento de Matemática Aplicada, UNED, Calle Juan del Rosal, 12, Ciudad Universitaria, Apartado 60149, 28080 Madrid, Spain; vnovo@ind.uned.es.
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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.

Keywords

Multiobjective optimization problemsconstraint qualificationnecessary conditions for Pareto minimumLagrange multiplierstangent coneDini differentiable functionsHadamard differentiable functionsquasiconvex functions.
Type
Research Article
Information
RAIRO - Operations Research , Volume 38 , Issue 3 , July 2004 , pp. 255 - 274
Copyright
© EDP Sciences, 2004

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