Some NP-complete problems in quadratic and nonlinear programming
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- Murty, K.G. & Kabadi, S.N. Mathematical Programming (1987) 39: 117. doi:10.1007/BF02592948
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a given feasible solution is not a local minimum, and
the objective function is not bounded below on the set of feasible solutions.
We construct a special class of indefinite quadratic programs, with simple constraints and integer data, and show that checking (a) or (b) on this class is NP-complete. As a corollary, we show that checking whether a given integer square matrix is not copositive, is NP-complete.