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Mathematical Methods of Operations Research

, Volume 60, Issue 1, pp 53–71 | Cite as

On the existence of solutions to systems of vector quasi-optimization problems

  • Nguyen Xuan Tan
Article
  • 64 Downloads

Abstract.

Some sufficient conditions for the existence of solutions to systems of vector quasi-optimization problems are given. These systems also include the systems of quasi-variational inequalities, quasi-equilibrium problems etc. As special case, we obtain some extensions for minimax theorems, general vector optimization problems, general vector quasi-optimization problems, quasi-equilibrium problems... concerning vector functions. From these we generalize some well-known results obtained by Blum and Oettli [4], Park [19], Chan and Pang[6], Parida and Sen [18], Browder and Minty [16], Ky Fan [8], etc.

Key words:

Systems of quasi-optimization problems Vector optimizations Quasi-equilibrium problems Ideal points Upper and lower C convex multi-valued mappings Strictly C-quasi-convex and Properly C-quasi-convex multi-valued mappings Upper and lower C-continuous multi-valued mappings 

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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  • Nguyen Xuan Tan
    • 1
  1. 1.Institute of MathematicsHanoiVietnam

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