Optimality conditions for mixed discrete bilevel optimization problems

In this article, we consider bilevel optimization problems with discrete lower level and continuous upper level problems. Taking into account both approaches (optimistic and pessimistic) which have been developed in the literature to deal with this type of problem, we derive some conditions for the...

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Bibliographic Details
Published in:Optimization 2018-06, Vol.67 (6), p.737-756
Main Authors: Dempe, S., Mefo Kue, F., Mehlitz, P.
Format: Article
Language:English
Subjects:
Bilevel programming
discrete parametric optimization
Mathematical programming
Nonlinear programming
optimality conditions
Optimization
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Summary:In this article, we consider bilevel optimization problems with discrete lower level and continuous upper level problems. Taking into account both approaches (optimistic and pessimistic) which have been developed in the literature to deal with this type of problem, we derive some conditions for the existence of solutions. In the case where the lower level is a parametric linear problem, the bilevel problem is transformed into a continuous one. After that, we are able to discuss local optimality conditions using tools of variational analysis for each of the different approaches. Finally, we consider a simple application of our results namely the bilevel programming problem with the minimum spanning tree problem in the lower level.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2018.1427092