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Second order optimality conditions for differentiable multiobjective problems

Published online by Cambridge University Press:  15 August 2002

Giancarlo Bigi  and
Marco Castellani
Giancarlo Bigi
Affiliation:
Dipartimento di Matematica, Università di Pisa, Italy.
Marco Castellani
Affiliation:
Dipartimento di Sistemi e Istituzioni per l'Economia, Università di L'Aquila, L'Aquila, Italy.
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Abstract

A second order optimality condition for multiobjective optimization with a set constraint is developed; this condition is expressed as the impossibility of nonhomogeneous linear systems. When the constraint is given in terms of inequalities and equalities, it can be turned into a John type multipliers rule, using a nonhomogeneous Motzkin Theorem of the Alternative. Adding weak second order regularity assumptions, Karush, Kuhn-Tucker type conditions are therefore deduced.

Keywords

Second order necessary optimality conditionsdescent directionssecond order contingent setAbadie and Guignard type conditions.
Type
Research Article
Information
RAIRO - Operations Research , Volume 34 , Issue 4 , October 2000 , pp. 411 - 426
Copyright
© EDP Sciences, 2000

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