Abstract
NP-hardness is established for the problem whose instance is a system of linear inequalities defining a polytopeP, and whose question is whether, onP, the global maximum of the Euclidean norm is attained at more than one vertex ofP. The NP-hardness persists even for the restricted problem in whichP is a full-dimensional parallelotope with one vertex at the origin. This makes it possible to establish NP-hardness for other uniqueness problems, including some from pseudoboolean programming and computational convexity.
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Research of the first author was supported in part by the Deutsche Forschungsgemeinschaft. Research of the second author was supported in part by the National Science Foundation.
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Gritzmann, P., Klee, V. Deciding uniqueness in norm maximization. Mathematical Programming 57, 203–214 (1992). https://doi.org/10.1007/BF01581081
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DOI: https://doi.org/10.1007/BF01581081