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Mixed-integer Quadratic Programming is in NP

Alberto Del Pia(alberto.delpia***at***gmail.com)
Santanu S. Dey(santanu.dey***at***isye.gatech.edu)
Marco Molinaro(molinaro***at***isye.gatech.edu)

Abstract: 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 and integer linear programming is in NP.

Keywords: Mixed-integer Quadratic Programming, Complexity, Size of Solution

Category 1: Integer Programming


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Entry Submitted: 07/17/2014
Entry Accepted: 07/17/2014
Entry Last Modified: 07/17/2014

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