Solving discrete linear bilevel optimization problems using the optimal value reformulation

S. Dempe () and F. Mefo Kue
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S. Dempe: TU Bergakademie Freiberg
F. Mefo Kue: TU Bergakademie Freiberg

Journal of Global Optimization, 2017, vol. 68, issue 2, No 2, 255-277

Abstract: Abstract In this article, we consider two classes of discrete bilevel optimization problems which have the peculiarity that the lower level variables do not affect the upper level constraints. In the first case, the objective functions are linear and the variables are discrete at both levels, and in the second case only the lower level variables are discrete and the objective function of the lower level is linear while the one of the upper level can be nonlinear. Algorithms for computing global optimal solutions using Branch and Cut and approximation of the optimal value function of the lower level are suggested. Their convergence is shown and we illustrate each algorithm via an example.

Keywords: Bilevel programming; Solution algorithm; Discrete parametric optimization; Global optimization; 90C11; 90C10; 90C29 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10898-016-0478-5

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