Variational Sets of Multivalued Mappings and a Unified Study of Optimality Conditions

  • P. Q. Khanh
  • N. D. Tuan


We propose two kinds of variational sets of any order for multivalued mappings and show that they are advantageous over many known generalized derivatives in the use for establishing optimality conditions. Applying these sets, we prove both necessary and sufficient optimality conditions of any order for efficiency and weak efficiency in a unified way. Many corollaries and examples are provided to show that our results include many recent existing ones. The imposed assumptions are very relaxed and the proofs are rather short in comparison with those of recent results in the literature.


Variational sets Multivalued mappings Nonsmooth vector optimization Efficiency Weak efficiency Optimality conditions Variational analysis 


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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsInternational University of Hochiminh CityHochiminh CityVietnam
  2. 2.Department of MathematicsUniversity of Natural Sciences of Hochiminh CityHochiminh CityVietnam

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