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Computational difficulties of bilevel linear programming. (English) Zbl 0708.90052
Summary: We show, using small examples, that two algorithms previously published for the bilevel linear programming problem (BLP) [see {\it J. F. Bard}, ibid. 31, 670-684 (1983; Zbl 0525.90086); and {\it W. F. Bialas} and {\it M. H. Karwan}, Manage. Sci. 30, 1004-1020 (1984; Zbl 0559.90053)] may fail to find the optimal solution and thus must be considered to be heuristics. A proof is given that solving BLP problems is NP-hard, which makes it unlikely that there is a good, exact algorithm.

90C05Linear programming
65K05Mathematical programming (numerical methods)
90C60Abstract computational complexity for mathematical programming problems
90-08Computational methods (optimization)
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