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New optimality conditions for the semivectorial bilevel optimization problem

Stephan Dempe(dempe***at***math.tu-freiberg.de)
Nazih Gadhi(ngadhi***at***hotmail.com)
Alain B. Zemkoho(zemkoho***at***daad-alumni.de)

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 rst-order necessary optimality conditions are then derived in the smooth and nonsmooth settings while using the generalized di erentiation calculus of Mordukhovich. Our approach is di erent from the one previously used in the literature and the conditions obtained are new and furthermore, they reduce to those of a usual bilevel program if the lower-level objective function becomes single-valued.

Keywords: Semivectorial bilevel optimization, multiojective optimization, weak efficient solution, optimal value function, optimality conditions

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Nonlinear Optimization

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )


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Entry Submitted: 11/03/2011
Entry Accepted: 11/03/2011
Entry Last Modified: 11/03/2011

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