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Journal of Convex Analysis 08 (2001), No. 2, 533--554
Copyright Heldermann Verlag 2001

Kuhn-Tucker Conditions and Integral Functionals

A. Bourass
Faculté des Sciences, Université Mohamed V, Rue Ibn Batouta, Rabat, Marocco

E. Giner
Laboratoire MIP, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse 04, France

Let X be a decomposable set, h a convex function defined on a finite dimensional vector space. We show that under transversality assumptions the problem of minimization on X: inf {f(x)+h(g(x))} admits Lagrange multipliers. We consider the case where f is a scalar integral functional and g is a vector valued integral functional. These properties are related to growth conditions between integrands.

Keywords: Performance function, multipliers, stability, convex like functions, measurable integrands, richness, integral functional, growth conditions.

MSC: 46E30; 28A20, 60B12

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