Mixed-integer Quadratic Programming is in NP
نویسندگان
چکیده
Mixed-integer quadratic programming (MIQP) 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 [11] and integer linear programming is in NP [1, 12, 4, 9].
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ورودعنوان ژورنال:
- Math. Program.
دوره 162 شماره
صفحات -
تاریخ انتشار 2017