Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T08:11:54.433Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)