Complexity of uniqueness and local search in quadratic 0-1 programming

@article{Pardalos1992ComplexityOU,
  title={Complexity of uniqueness and local search in quadratic 0-1 programming},
  author={Panos M. Pardalos and Somesh Jha},
  journal={Oper. Res. Lett.},
  year={1992},
  volume={11},
  pages={119-123}
}
We prove that the problem of checking whether a quadratic 0-1 problem has a unique solution is NP-hard. Furthermore, we prove that finding the global minimum of quadratic 0-1 programming with unique solution remains an NP-hard problem. Regarding local search, we prove that the problem of finding a discrete local minimum for quadratic 0-1 problems, with two coordinates being fixed, is NP-hard. In addition, we discuss an algorithm for computing discrete local minima. 

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