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# Nonconvex quadratic reformulations and solvable conditions for mixed integer quadratic programming problems

• In this paper, we study a mixed integer constrained quadratic programming problem. This problem is NP-Hard. By reformulating the problem to a box constrained quadratic programming and solving the reformulated problem, we can obtain a global optimal solution of a sub-class of the original problem. The reformulated problem may not be convex and may not be solvable in polynomial time. Then we propose a solvability condition for the reformulated problem, and discuss methods to construct a solvable reformulation for the original problem. The reformulation methods identify a solvable subclass of the mixed integer constrained quadratic programming problem.
Mathematics Subject Classification: Primary: 90C26, 90C20, 90C11; Secondary: 49M37.

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