Journal of Global Optimization

, Volume 61, Issue 4, pp 745–767 | Cite as

On set-valued optimization problems with variable ordering structure



In this paper we introduce and investigate an optimality concept for set-valued optimization problems with variable ordering structure. In our approach, the ordering structure is governed by a set-valued map acting between the same spaces as the objective multifunction. Necessary optimality conditions for the proposed problem are derived in terms of Bouligand and Mordukhovich generalized differentiation objects.


Nondomination property Pareto optimization Variable ordering structure Openness for sum-multifunction Necessary optimality conditions 

Mathematics Subject Classification

90C30 49J52 49J53 



The work of M. Durea was supported by the ERC-Like grant of the Romanian National Authority for Scientific Research 1ERC/02.07.2012. The work of R. Strugariu was supported by the grant POSDRU/159/1.5/S/133652.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Marius Durea
    • 1
  • Radu Strugariu
    • 2
  • Christiane Tammer
    • 3
  1. 1.Faculty of Mathematics“Al. I. Cuza” UniversityIaşiRomania
  2. 2.Department of Mathematics and Informatics“Gh. Asachi” Technical UniversityIaşiRomania
  3. 3.Institute for MathematicsMartin-Luther-University Halle-WittenbergHalle (Saale)Germany

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