Wang, Zhenbo; Fang, Shu-Cherng; Gao, David Y.; Xing, Wenxun Global extremal conditions for multi-integer quadratic programming. (English) Zbl 1161.90457 J. Ind. Manag. Optim. 4, No. 2, 213-225 (2008). Summary: 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 \(p (\geq 3)\) 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. Cited in 17 Documents MSC: 90C20 Quadratic programming 90C10 Integer programming 90C46 Optimality conditions and duality in mathematical programming Keywords:global optimization; quadratic programming; duality theory PDF BibTeX XML Cite \textit{Z. Wang} et al., J. Ind. Manag. Optim. 4, No. 2, 213--225 (2008; Zbl 1161.90457) Full Text: DOI Link OpenURL