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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

Roberto Lucchetti
Dip. di Matematica, Politecnico di Milano, Via Bonardi 7, 20133 Milano, Italy

Nadezhda Ribarska
Dept. of Mathematics and Informatics, Sofia University, James Bourchier Boul. 5, 1126 Sofia, Bulgaria

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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