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2008, Volume 4, Issue 2: 213-225. Doi: 10.3934/jimo.2008.4.213
This issue Previous Article Next Article Finite difference approximation for stochastic optimal stopping problems with delays

Global extremal conditions for multi-integer quadratic programming

  • 1.

    Department of Mathematical Sciences, Tsinghua University, Beijing

  • 2.

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

  • 3.

    Department of Mathematics, Virginia Tech, Blacksburgh, VA

Received:  August 31, 2007
Revised:  December 31, 2007
Published:  March 2008
Abstract Related Papers Cited by
    Abstract
  • 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.

    Citation:
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