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New Optimality Conditions for the Semivectorial Bilevel Optimization Problem

  • S. Dempe
  • N. Gadhi
  • A. B. Zemkoho
Article

Abstract

The paper is concerned with the optimistic formulation of a bilevel optimization problem with multiobjective lower-level problem. Considering the scalarization approach for the multiobjective program, we transform our problem into a scalar-objective optimization problem with inequality constraints by means of the well-known optimal value reformulation. Completely detailed first-order necessary optimality conditions are then derived in the smooth and nonsmooth settings while using the generalized differentiation calculus of Mordukhovich. Our approach is different from the one previously used in the literature and the conditions obtained are new. Furthermore, they reduce to those of a usual bilevel program, if the lower-level objective function becomes single-valued.

Keywords

Semivectorial bilevel optimization Multiobjective optimization Weakly efficient solution Optimal value function Optimality conditions 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTU Bergakademie FreibergFreibergGermany
  2. 2.Department of MathematicsDhar El Mehrez, Sidi Mohamed Ben Abdellah UniversityFesMorocco

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