Exact and approximate vector Ekeland variational principles

Abstract

This paper concerns with exact and approximate Ekeland variational principles for vector-valued functions and bifunctions that are derived via linear and nonlinear scalarization processes by an approximate scalar formulation of the Ekeland variational principle and a revised version of Dancs–Hegedüs–Medvegyev's fixed point theorem. Both results are also interesting in themselves and involve really mild assumptions. As a result, the obtained Ekeland variational principles improve some recent results in the literature since weaker assumptions are required.

Keywords:

• Ekeland variational principle
• Dancs–Hegedüs–Medvegyev's fixed point theorem
• vector optimization
• scalarization
• strictly decreasing cone lower semicontinuity

2010 Mathematics Subject Classifications:

• 47H10
• 49J53
• 90C29

Acknowledgments

The first author wishes to thank Department of Applied Mathematics for the very warm hospitality during his visit at Universidad Nacional de Educación a Distancia, Madrid and the Humboldt Foundation for financial support.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work, for the last three authors, was partially supported by the Ministerio de Ciencia, Innovación y Universidades (MCIU), Agencia Estatal de Investigación (AEI) (Spain) and Fondo Europeo de Desarrollo Regional (FEDER) under project PGC2018-096899-B-I00 (MCIU/AEI/FEDER, UE).