Journal of Optimization Theory and Applications

, Volume 130, Issue 2, pp 185–207 | Cite as

Characterization of the Nonemptiness and Compactness of Solution Sets in Convex and Nonconvex Vector Optimization

  • F. Flores-Bazán
  • C. Vera


As a consequence of an abstract theorem proved elsewhere, a vector Weierstrass theorem for the existence of a weakly efficient solution without any convexity assumption is established. By using the notion (recently introduced in an earlier paper) of semistrict quasiconvexity for vector functions and assuming additional structure on the space, new existence results encompassing many results appearing in the literature are derived. Also, when the cone defining the preference relation satisfies some mild assumptions (but including the polyhedral and icecream cones), various characterizations for the nonemptiness and compactness of the weakly efficient solution set to convex vector optimization problems are given. Similar results for a class of nonconvex problems on the real line are established as well.


Nonconvex vector optimization quasiconvex vector functions weakly efficient solutions efficient solutions asymptotic functions asymptotic cones 


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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • F. Flores-Bazán
    • 1
  • C. Vera
    • 1
  1. 1.Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y MatemáticasUniversidad de ConcepciónConcepciónChile

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