Some NP-complete problems in quadratic and nonlinear programming

  title={Some NP-complete problems in quadratic and nonlinear programming},
  author={Katta G. Murty and Santosh N. Kabadi},
  journal={Mathematical Programming},
AbstractIn continuous variable, smooth, nonconvex nonlinear programming, we analyze the complexity of checking whether(a)a given feasible solution is not a local minimum, and(b)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… Expand
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