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Approximate Saddle Point Assertions for a General Class of Approximation Problems

  • W. W. Breckner
  • M. Sekatzek
  • Chr. Tammer

Abstract

We consider a vector-valued approximation problem, where the objective function is defined by sub inear mappings f : XR p . Using a generalized Lagrangean we derive necessary and sufficient conditions for approximate saddle points of this Lagrangean. Especially, we prove an approximate complementary slackness condition. Furthermore, we compute the approximation error with respect to the original problem. We show the results on the base of a scalarization with linear continuous functionals.

Keywords

Saddle Point Approximation Problem Vector Optimization Vector Optimization Problem Topological Linear Space 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • W. W. Breckner
    • 1
  • M. Sekatzek
    • 2
  • Chr. Tammer
    • 2
  1. 1.Faculty of Mathematics and Computer ScienceBabeş-Bolyai UniversityCluj-NapocaRomania
  2. 2.Department of Mathematics and Computer ScienceMartin Luther University Halle-WittenbergHalle/SaaleGermany

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