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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 setdefined by inequality and equality constraints such that all functionsare, at least, Dini differentiable (in some cases, Hadamard differentiableand sometimes, quasiconvex). Several constraint qualifications are givenin such a way that generalize both the qualifications introduced by Maedaand the classical ones, when the functions are differentiable. Therelationships between them are analyzed. Finally, we give severalKuhn-Tucker type necessary conditions for a point to be Pareto minimumunder the weaker constraint qualifications here proposed.

Keywords

Multiobjective optimization problemsconstraint qualificationnecessaryconditions for Pareto minimumLagrange multiplierstangent coneDinidifferentiable functionsHadamard differentiable functionsquasiconvexfunctions.

Information

Type
Research Article
Information
RAIRO - Operations Research , Volume 38 , Issue 3 , July 2004 , pp. 255 - 274
Copyright
© EDP Sciences, 2004

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