American Institute of Mathematical Sciences

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April  2008, 4(2): 213-225. doi: 10.3934/jimo.2008.4.213

Global extremal conditions for multi-integer quadratic programming

Zhenbo Wang 1, , Shu-Cherng Fang 2, , David Y. Gao 3, and  Wenxun Xing 1,

1. 

Department of Mathematical Sciences, Tsinghua University, Beijing, China
2. 

Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC
3. 

Department of Mathematics, Virginia Tech, Blacksburgh, VA

Received  September 2007 Revised  January 2008 Published  April 2008

This paper presents a canonical duality approach to solve an integer quadratic programming problem, in which the objective function is quadratic and each variable may assume the value of one of $p~( \ge 3)$ integers. We first transform the problem into a $\{-1,1\}$ integer quadratic programming problem and then derive its ''canonical dual''. It is shown that, under certain conditions, this nonconvex multi-integer programming problem is equivalent to a concave maximization dual problem over a convex feasible domain. A global optimality condition is derived and some computational examples are provided to illustrate this approach.
Keywords: quadratic programming, Global optimization, duality theory..
Mathematics Subject Classification: Primary: 49N15, 49M37, 90C26, 90C2.
Citation: Zhenbo Wang, Shu-Cherng Fang, David Y. Gao, Wenxun Xing. Global extremal conditions for multi-integer quadratic programming. Journal of Industrial and Management Optimization, 2008, 4 (2) : 213-225. doi: 10.3934/jimo.2008.4.213
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