Application of a Vector-Valued Ekeland-Type Variational Principle for Deriving Optimality Conditions

  • G. Isac
  • C. Tammer
Part of the Springer Optimization and Its Applications book series (SOIA, volume 35)


In order to show necessary conditions for approximate solutions of vector-valued optimization problems in general spaces, we introduce an axiomatic approach for a scalarization scheme. Several examples illustrate this scalarization scheme. Using an Ekeland-type variational principle by Isac [12] and suitable scalarization techniques, we prove the optimality conditions under different assumptions concerning the ordering cone and under certain differentiability assumptions for the objective function.


Risk Measure Convex Cone Topological Vector Space Vector Optimization Problem Closed Convex Cone 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • G. Isac
    • 1
  • C. Tammer
    • 2
  1. 1.Department of Mathematics and Computer ScienceRoyal Military College of CanadaSTN Forces KingstonCanada
  2. 2.Institute of MathematicsMartin-Luther-University Halle-WittenbergHalleGermany

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