Geodesic
Alternative Theorems and Necessary Optimality Conditions for Directionally Differentiable Multiobjective Programs
Journal of convex analysis, Tome 9 (2002) no. 1, pp. 97-116.

Voir la notice de l'article provenant de la source Heldermann Verlag

We study, in a unified way, some alternative theorems that involve linear and sublinear functions between finite dimensional spaces and a convex set, and we propose several generalizations of them. These theorems are applied to obtain, under different constraint qualifications, several necessary conditions for a point to be Pareto optimum, both Fritz John and Kuhn-Tucker type, in multiobjective programming problems which are defined by directionally differentiable functions and which include three types of constraints: inequality, equality and set constraints. In particular, these necessary conditions are applicable to convex programs and to differentiable programs.
Classification : 90C29, 90C46
Mots-clés : Multiobjective programming, alternative theorems, necessary conditions for Pareto minimum, Lagrange multipliers 
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     title = {Alternative {Theorems} and {Necessary} {Optimality} {Conditions} for {Directionally} {Differentiable} {Multiobjective} {Programs}},
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B. Jiménez; V. Novo. Alternative Theorems and Necessary Optimality Conditions for Directionally Differentiable Multiobjective Programs. Journal of convex analysis, Tome 9 (2002) no. 1, pp. 97-116. http://geodesic.mathdoc.fr/item/JCA_2002_9_1_JCA_2002_9_1_a4/