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27 Vertex With Specified Objective Value

Input: H-description of a polyhedron P Ì Qd, c Î Qd, C Î Q
Output: "Yes" if there is a vertex v of P with cTv = C; "No" otherwise
Status (general): Strongly NP-complete
Status (fixed dim.): Polynomial time
Proved to be NP-complete by Chandrasekaran, Kabadi, and Murty [11] and strongly NP-complete by Fukuda, Liebling, and Margot [22]. The problem remains strongly NP-complete even if the input is restricted to polytopes [22].