Recent work has demonstrated the potential for globally optimizing nonconvex quadratic programs using a reformulation based on the first order optimality conditions. We show how this reformulation may be generalized to account for fixed cost variables. We then extend some of the polyhedral work that has been done for bound constrained QPs to handle such fixed cost variables. We show how to lift known classes of inequalities for the case without fixed cost variables and propose several new classes. These inequalities are incorporated in a branch-and-cut algorithm.
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