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Global Optimization Techniques for Solving the General Quadratic Integer Programming Problem
Authors:Nguyen Van Thoai
Affiliation:(1) Department of Mathematics, University of Trier, 54286 Trier, Germany
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 ldquointegral rectangular partitionrdquo, 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.
Keywords:quadratic integer programming  branch and bound algorithms  concave minimization  global optimization
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