Mixed-integer quadratic programming is in NP

@article{Pia2014MixedintegerQP,
  title={Mixed-integer quadratic programming is in NP},
  author={Alberto Del Pia and Santanu S. Dey and Marco Molinaro},
  journal={Mathematical Programming},
  year={2014},
  volume={162},
  pages={225-240}
}
Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of mixed-integer quadratic programming is in NP, thereby showing that it is NP-complete. This is established by showing that if the decision version of mixed-integer quadratic programming is feasible, then there exists a solution of polynomial size. This result… CONTINUE READING

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