Cyclically antimonotone vector equilibrium problems

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.

KEYWORDS:

• Ekeland's variational principle
• cyclic antimonotonicity
• vector triangle inequality
• level K-lower semicontinuity
• vector equilibria

Acknowledgments

The author is grateful to the anonymous referees for their valuable suggestions and remarks that helped her to improve the first version of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of the author was supported by a grant of Romanian Ministry of Research and Innovation, CNCS -UEFISCDI, project number PN-III-P4-ID-PCE-2016-0190, within PNCDI III.