Second order optimality conditions for bilevel set optimization problems

Authors:
S. Dempe;N. Gadhi
Affiliations:
Department of Mathematics and Computer Sciences, Technical University Bergakademie Freiberg, Freiberg, Germany;Dhar El Mehrez, Department of Mathematics, Sidi Mohamed Ben Abdellah University, Fes, Morocco
Venue:
Journal of Global Optimization
Year:
2010

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Abstract

In this work, we use the notion of the support function to the feasible set mapping to establish second order necessary and sufficient optimality conditions for the optimistic case of bilevel optimization problems. The main tools we exploit are approximate Jacobians, approximate Hessians, second order approximations and second order contingent sets.