Global optimization of a quadratic function subject to a bounded mixed integer consraint set |
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Authors: | Faiz A. Al-Khayyal Christian Larsen |
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Affiliation: | (1) School of Industrial and Systems Engineering, Georgia Institute of Technology, 30332-0205 Atlanta, GA, USA;(2) Department of Operations Research, University of Aarhus, Denmark |
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Abstract: | In this paper we consider the optimization of a quadratic function subject to a linearly bounded mixed integer constraint set. We develop two types of piecewise affine convex underestimating functions for the objective function. These are used in a branch and bound algorithm for solving the original problem. We show finite convergence to a near optimal solution for this algorithm. We illustrate the algorithm with a small numerical example. Finally we discuss some modifications of the algorithm and address the question of extending the problem to include quadratic constraints.Supported by grants from the Danish Natural Science Research Council and the Danish Research Academy. |
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