Volume 34, Number 4, October December 2000
|Page(s)||411 - 426|
|Published online||15 August 2002|
Second order optimality conditions for differentiable multiobjective problems
Dipartimento di Matematica,
Università di Pisa, Italy.
2 Dipartimento di Sistemi e Istituzioni per l'Economia, Università di L'Aquila, L'Aquila, Italy.
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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