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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Trier, 54286, Trier, Germany

    Nguyen Van Thoai

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  1. Nguyen Van Thoai
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Thoai, N.V. Global Optimization Techniques for Solving the General Quadratic Integer Programming Problem. Computational Optimization and Applications 10, 149–163 (1998). https://doi.org/10.1023/A:1018364802456

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