Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs

M. Köppe (), M. Queyranne () and C. T. Ryan ()
Additional contact information
M. Köppe: University of California
M. Queyranne: Universidad de Chile
C. T. Ryan: Sauder School of Business at the University of British Columbia

Journal of Optimization Theory and Applications, 2010, vol. 146, issue 1, No 9, 137-150

Abstract: Abstract We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and mixed integer bilevel problems. For the mixed integer case where the leader’s variables are continuous, our algorithm also detects whether the infimum cost fails to be attained, a difficulty that has been identified but not directly addressed in the literature. In this case, it yields a “better than fully polynomial time” approximation scheme with running time polynomial in the logarithm of the absolute precision. For the pure integer case where the leader’s variables are integer, and hence optimal solutions are guaranteed to exist, we present an algorithm which runs in polynomial time when the total number of variables is fixed.

Keywords: Bilevel mixed integer linear programming; Parametric integer linear programming; Computational complexity; Binary search (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (17)

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DOI: 10.1007/s10957-010-9668-3

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