Optimality conditions for mixed discrete bilevel optimization problems. (3rd June 2018)

• Record Type: Journal Article
• Authors: Dempe, S.; Mefo Kue, F.; Mehlitz, P.
• Is Part Of: Optimization. Volume 67:Number 6(2018)
• Page Start: 737
• Page End: 756
• Publication Date: 2018-06-03
• Subjects: Bilevel programming -- discrete parametric optimization -- optimality conditions; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1427092
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: 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.