Optimality Conditions Without Continuity in Multivalued Optimization Using Approximations as Generalized Derivatives

Part of the Springer Optimization and Its Applications book series (SOIA, volume 50)


We propose a notion of approximations as generalized derivatives for multivalued mappings and establish both necessary and sufficient conditions of orders 1 and 2 for various kinds of efficiency in multivalued vector optimization without convexity and even continuity. Compactness assumptions are also relaxed. Our theorems include several recent existing results in the literature as special cases.


Vector Optimization Generalize Derivative Compactness Assumption Recession Cone Differentiability Assumption 
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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsInternational University of Hochiminh CityHochiminh CityVietnam
  2. 2.Department of Mathematics and StatisticsUniversity of Economics of Hochiminh CityHochiminh CityVietnam

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