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Mixed-integer Quadratic Programming is in NP

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 generalizes and unifies classical results that quadratic programming is in NP and integer linear programming is in NP.

preprint2014arXivOpen access
Alberto Del PiaSantanu S. DeyMarco Molinaro
math.CODiscrete Mathematics
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Alberto Del PiaSantanu S. DeyMarco Molinaro

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