Optimization Letters

, Volume 12, Issue 3, pp 615–623 | Cite as

A note on existence of weak efficient solutions for vector equilibrium problems

  • C. Gutiérrez
  • V. Novo
  • J. L. Ródenas-Pedregosa
Original Paper


This work concerns with vector equilibrium problems where the image space of the bifunction is not endowed with any topology. To be precise, a kind of “semi-algebraic” upper semicontinuity notion is introduced and, by means of a recent algebraic version of the so-called Gerstewitz’s functional, a new existence result of weak efficient solutions is obtained that significantly improves some previous ones stated in the topological setting since it requires weaker assumptions.


Vector equilibrium problem Algebraic interior Gerstewitz’s functional Triangle inequality property Semicontinuity 



The authors are grateful to the anonymous referee for his/her useful suggestions and remarks. This work was partially supported by Ministerio de Economía y Competitividad (Spain) under Project MTM2015-68103-P (MINECO/FEDER) and by ETSI Industriales, Universidad Nacional de Educación a Distancia (Spain) under Grant 2017-Mat11. Third author was also supported by Spanish FPI Fellowship Programme (BES-2013-066316).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • C. Gutiérrez
    • 1
  • V. Novo
    • 2
  • J. L. Ródenas-Pedregosa
    • 2
  1. 1.IMUVA (Institute of Mathematics of University of Valladolid)ValladolidSpain
  2. 2.Departamento de Matemática Aplicada, E.T.S.I. IndustrialesUniversidad Nacional de Educación a DistanciaMadridSpain

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