On constraint qualifications in directionally differentiable multiobjective optimization problems
Dipartimento di Ricerche Aziendali, Università
degli Studi di Pavia, Via S. Felice, 5, 27100 Pavia, Italy; firstname.lastname@example.org.
2 Departamento de Economía e Historia Económica, Facultad de Economía y Empresa, Universidad de Salamanca, Campus Miguel de Unamuno, s/n, 37007 Salamanca, Spain; email@example.com.
3 Departamento de Matemática Aplicada, UNED, Calle Juan del Rosal, 12, Ciudad Universitaria, Apartado 60149, 28080 Madrid, Spain; firstname.lastname@example.org.
Accepted: 25 March 2004
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.
Mathematics Subject Classification: 90C29 / 90C46
Key words: Multiobjective optimization problems / constraint qualification / necessary conditions for Pareto minimum / Lagrange multipliers / tangent cone / Dini differentiable functions / Hadamard differentiable functions / quasiconvex functions.
© EDP Sciences, 2004