, Volume 18, Issue 3, pp 531–556 | Cite as

Efficiency in vector quasi-equilibrium problems and applications

  • Nguyen Ba Minh
  • Le Anh TuanEmail author
  • Pham Huu Sach


In this paper, we give sufficient conditions for the existence of efficient solutions of a generalized vector quasi-equilibrium problem in topological vector spaces. The motivations for introducing this problem come from practical problems in traffic networks and the optimal control theory for discrete-time dynamical systems. The main results of the paper are proven with the help of a strongly monotonic function which can be constructed from the data of the problem under consideration. Some notions of cone-semicontinuity of set-valued maps, weaker than the usual concepts of semicontinuity, are also used in our study. As applications, we obtain existence results in vector quasi-optimization problems, Stampacchia set-valued vector quasi-variational inequality problems and Pareto vector quasi-saddle point problems. All these results are different from the corresponding ones in the literature.


Vector quasi-equilibrium problem Optimal control theory  Vector quasi-optimization problem Pareto vector quasi-saddle point  Cone-semicontinuity Set-valued map 

Mathematics Subject Classification (2000)

49J53 54H25 



This research is funded by Vietnam National Foundation for Science and Technology (NAFOSTED).


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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Nguyen Ba Minh
    • 1
  • Le Anh Tuan
    • 2
    • 3
    Email author
  • Pham Huu Sach
    • 4
  1. 1.Hanoi University of CommerceHanoiVietnam
  2. 2.Nong Lam UniversityHo Chi Minh CityVietnam
  3. 3.Ninh Thuan College of PedagogyNinh ThuanVietnam
  4. 4.Hanoi Institute of Mathematics, Vietnam Academy of Science and TechnologyHanoiVietnam

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