# Global Optimization Techniques for Solving the General Quadratic Integer Programming Problem

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## Abstract

We consider the problem of minimizing a general quadratic function over a polytope in the *n*-dimensional space with integrality restrictions on all of the variables. (This class of problems contains, e.g., the quadratic 0-1 program as a special case.) A finite branch and bound algorithm is established, in which the branching procedure is the so-called “integral rectangular partition”, and the bound estimation is performed by solving a concave programming problem with a special structure. Three methods for solving this special concave program are proposed.

quadratic integer programming branch and bound algorithms concave minimization global optimization

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© Kluwer Academic Publishers 1998