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Linear transformation based solution methods for non-convex mixed integer quadratic programs

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Abstract

Two preprocessing techniques for mixed integer quadratic programs with non-convex objective functions are presented. The first is a convexification scheme and can be applied to problems were the continuous part of the Hessian is positive semidefinite. The second technique aims to reduce the size of the underestimating problems solved by branch-and-bound algorithms and can be applied to problems were the continuous part of the Hessian is singular. Numerical results are presented showing the effect of the preprocessing techniques.

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Acknowledgments

The second author would also like to thank Professor Tapio Westerlund of Åbo Academi, Turku, Finland, for introducing the research area to him. Financial support was provided by the National Research Foundation of South Africa under Grant CPR2010030300009918.

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Authors and Affiliations

  1. School of Computer Science and Applied Mathematics, Faculty of Science, University of the Witwatersrand, Wits, 2050, South Africa

    Eric Newby

  2. TCSE, Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, South Africa

    M. M. Ali

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  1. Eric Newby
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  2. M. M. Ali
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Correspondence to M. M. Ali.

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Newby, E., Ali, M.M. Linear transformation based solution methods for non-convex mixed integer quadratic programs. Optim Lett 11, 967–981 (2017). https://doi.org/10.1007/s11590-015-0988-y

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  • DOI: https://doi.org/10.1007/s11590-015-0988-y

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