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Minimizing rational functions by exact Jacobian SDP relaxation applicable to finite singularities

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  • Feng Guo
  • Li Wang
  • Guangming Zhou

Abstract

This paper considers the optimization problem of minimizing a rational function. We reformulate this problem as a polynomial optimization problem by the technique of homogenization. These two problems are shown to be equivalent under some generic conditions. The exact Jacobian SDP relaxation method proposed by Nie is used to solve the resulting polynomial optimization problem. We also prove that the assumption of nonsingularity in Nie’s method can be weakened to the finiteness of singularities. Some numerical examples are given in the end. Copyright Springer Science+Business Media New York 2014

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  • Feng Guo & Li Wang & Guangming Zhou, 2014. "Minimizing rational functions by exact Jacobian SDP relaxation applicable to finite singularities," Journal of Global Optimization, Springer, vol. 58(2), pages 261-284, February.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:2:p:261-284
    DOI: 10.1007/s10898-013-0047-0
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    References listed on IDEAS

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    1. Jibetean, D. & de Klerk, E., 2006. "Global optimization of rational functions : A semidefinite programming approach," Other publications TiSEM 25febbc3-cd0c-4eb7-9d37-d, Tilburg University, School of Economics and Management.
    2. Laurent, M., 2009. "Sums of squares, moment matrices and optimization over polynomials," Other publications TiSEM 9fef820b-69d2-43f2-a501-e, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Guangming Zhou & Qin Wang & Wenjie Zhao, 2020. "Saddle points of rational functions," Computational Optimization and Applications, Springer, vol. 75(3), pages 817-832, April.

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