, Volume 68, Issue 2, pp 371-378

Some properties of the bilevel programming problem

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The purpose of this paper is to elaborate on the difficulties accompanying the development of efficient algorithms for solving the bilevel programming problem (BLPP). We begin with a pair of examples showing that, even under the best of circumstances, solutions may not exist. This is followed by a proof that the BLPP is NP-hard.

Communicated by M. Avriel
This work was partially supported by a grant from the Advanced Research Program of the Texas Higher Education Coordinating Board.