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Journal of Convex Analysis 09 (2002), No. 2, 415--428
Copyright Heldermann Verlag 2002



Critical Point Theory for Vector Valued Functions

Marco Degiovanni
Dip. di Matematica e Fisica, UniversitÓ Cattolica del Sacro Cuore, Via Dei Musei 41, 25121 Brescia, Italy
m.degiovanni@dmf.unicatt.it

Roberto Lucchetti
Dip. di Matematica, Politecnico di Milano, Via Bonardi 7, 20133 Milano, Italy
rel@komodo.ing.unico.it

Nadezhda Ribarska
Dept. of Mathematics and Informatics, Sofia University, James Bourchier Boul. 5, 1126 Sofia, Bulgaria
ribarska@fmi.uni-sofia.bg



We consider a continuous function defined on a metric space with values in a Banach space endowed with an order cone. In this setting, we provide an extension of min-max techniques, such as the Mountain pass theorem and Ljusternik-Schnirelman theory, without assuming the order cone to have nonempty interior.

Keywords: Vector optimization, nonsmooth critical point theory.

MSC: 49J40; 58E05

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