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October  2011, 7(4): 1027-1039. doi: 10.3934/jimo.2011.7.1027

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

 1 Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27606, United States 2 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received  October 2010 Revised  July 2011 Published  August 2011

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.
Citation: Ye Tian, Cheng Lu. Nonconvex quadratic reformulations and solvable conditions for mixed integer quadratic programming problems. Journal of Industrial & Management Optimization, 2011, 7 (4) : 1027-1039. doi: 10.3934/jimo.2011.7.1027
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