Issue |
RAIRO-Oper. Res.
Volume 34, Number 4, October December 2000
|
|
---|---|---|
Page(s) | 411 - 426 | |
DOI | https://doi.org/10.1051/ro:2000122 | |
Published online | 15 August 2002 |
Second order optimality conditions for differentiable multiobjective problems
1
Dipartimento di Matematica,
Università di Pisa, Italy.
2
Dipartimento di Sistemi e
Istituzioni per l'Economia,
Università di L'Aquila, L'Aquila, Italy.
Received:
18
December
1999
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.
Key words: Second order necessary optimality conditions / descent directions / second order contingent set / Abadie and Guignard type conditions.
© EDP Sciences, 2000
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