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Global extremal conditions for multi-integer quadratic programming

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  • 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.
    Mathematics Subject Classification: Primary: 49N15, 49M37, 90C26, 90C20.


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