Cyclically antimonotone vector equilibrium problems. (2nd December 2018)

• Record Type: Journal Article
• Authors: Miholca, Mihaela
• Is Part Of: Optimization. Volume 67:Number 12(2018)
• Page Start: 2191
• Page End: 2204
• Publication Date: 2018-12-02
• Subjects: Ekeland's variational principle -- cyclic antimonotonicity -- vector triangle inequality -- level K-lower semicontinuity -- vector equilibria; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1523405
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we extend the notion of cyclic antimonotonicity (known for scalar bifunctions) to the vector case, in order to obtain a vectorial equilibrium version of Ekeland's variational principle. We characterize the cyclic antimonotonicity in terms of a suitable approximation from below of the vector bifunction, which allows us to avoid the demanding triangle inequality property, usually required in the literature, when dealing with Ekeland's principle for bifunctions. Furthermore, a result for weak vector equilibria in the absence of convexity assumptions is given, without passing through the existence of approximate solutions.