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Nonconvex min–max fractional quadratic problems under quadratic constraints: copositive relaxations

Author

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  • Paula Alexandra Amaral

    (Universidade Nova de Lisboa)

  • Immanuel M. Bomze

    (Universität Wien)

Abstract

In this paper we address a min–max problem of fractional quadratic (not necessarily convex) over linear functions on a feasible set described by linear and (not necessarily convex) quadratic functions. We propose a conic reformulation on the cone of completely positive matrices. By relaxation, a doubly nonnegative conic formulation is used to provide lower bounds with evidence of very small gaps. It is known that in many solvers using Branch and Bound the optimal solution is obtained in early stages and a heavy computational price is paid in the next iterations to obtain the optimality certificate. To reduce this effort tight lower bounds are crucial. We will show empirical evidence that lower bounds provided by the copositive relaxation are able to substantially speed up a well known solver in obtaining the optimality certificate.

Suggested Citation

  • Paula Alexandra Amaral & Immanuel M. Bomze, 2019. "Nonconvex min–max fractional quadratic problems under quadratic constraints: copositive relaxations," Journal of Global Optimization, Springer, vol. 75(2), pages 227-245, October.
    • Handle: RePEc:spr:jglopt:v:75:y:2019:i:2:d:10.1007_s10898-019-00780-3
    DOI: 10.1007/s10898-019-00780-3
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    References listed on IDEAS

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    Cited by:

    1. Zhijun Xu & Jing Zhou, 2021. "A Global Optimization Algorithm for Solving Linearly Constrained Quadratic Fractional Problems," Mathematics, MDPI, vol. 9(22), pages 1-12, November.

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