Linear bilevel multi-follower programming with independent followers |
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Authors: | Herminia I Calvete Carmen Galé |
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Institution: | (1) Dpto. de Métodos Estadísticos, Universidad de Zaragoza, Pedro Cerbuna, 12, 50009 Zaragoza, Spain |
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Abstract: | This paper considers a particular case of linear bilevel programming problems with one leader and multiple followers. In this
model, the followers are independent, meaning that the objective function and the set of constraints of each follower only
include the leader’s variables and his own variables. We prove that this problem can be reformulated into a linear bilevel
problem with one leader and one follower by defining an adequate second level objective function and constraint region. In
the second part of the paper we show that the results on the optimality of the linear bilevel problem with multiple independent
followers presented in Shi et al. The kth-best approach for linear bilevel multi-follower programming, J. Global Optim. 33, 563–578 (2005)] are based on a misconstruction
of the inducible region. |
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Keywords: | Bilevel programming Linear Multiple followers kth-best |
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