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A trajectory-based method for mixed integer nonlinear programming problems

Author

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  • Terry-Leigh Oliphant

    (School of Computer Science and Applied Mathematics
    University of the Witwatersrand)

  • M. Montaz Ali

    (School of Computer Science and Applied Mathematics
    Faculty of Engineering and Built Environment
    University of the Witwatersrand)

Abstract

A local trajectory-based method for solving mixed integer nonlinear programming problems is proposed. The method is based on the trajectory-based method for continuous optimization problems. The method has three phases, each of which performs continuous minimizations via the solution of systems of differential equations. A number of novel contributions, such as an adaptive step size strategy for numerical integration and a strategy for updating the penalty parameter, are introduced. We have shown that the optimal value obtained by the proposed method is at least as good as the minimizer predicted by a recent definition of a mixed integer local minimizer. Computational results are presented, showing the effectiveness of the method.

Suggested Citation

  • Terry-Leigh Oliphant & M. Montaz Ali, 2018. "A trajectory-based method for mixed integer nonlinear programming problems," Journal of Global Optimization, Springer, vol. 70(3), pages 601-623, March.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:3:d:10.1007_s10898-017-0570-5
    DOI: 10.1007/s10898-017-0570-5
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    References listed on IDEAS

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    1. Kumar Abhishek & Sven Leyffer & Jeff Linderoth, 2010. "FilMINT: An Outer Approximation-Based Solver for Convex Mixed-Integer Nonlinear Programs," INFORMS Journal on Computing, INFORMS, vol. 22(4), pages 555-567, November.
    2. Ernesto Birgin & J. Martínez, 2012. "Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization," Computational Optimization and Applications, Springer, vol. 51(3), pages 941-965, April.
    3. S.-P. Han, 1986. "On the Augmented Lagrangian," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 161-168, February.
    4. Eric Newby & M. M. Ali, 2014. "A Note on Convex Reformulation Schemes for Mixed Integer Quadratic Programs," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 457-469, February.
    5. Eric Newby & M. Montaz Ali, 2016. "Transformation-Based Preprocessing for Mixed-Integer Quadratic Programs," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 1039-1045, March.
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