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On Search for All Roots of a System of Quadratic Equations

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Optimization and Applications (OPTIMA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13078))

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Abstract

We propose an approach to finding the roots of systems of quadratic equations in a box. This approach is based on a reduction to an auxiliary optimization problem. The auxiliary problem turns out to be, in general, a nonconvex optimization problem, with the objective function and inequality constraints given by d.c. functions. We use the linearization technique with respect to the basic nonconvexity and box partition procedure to try to find all solutions of the system or proof that there are no solutions in the box. The results of the computational simulation are given.

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Acknowledgments

The authors would like to thank the reviewers for their work and valuable comments.

The research was carried out under State Assignment Projects (no. FWEU-2021-0006, FWEW-2021-0003) of the Fundamental Research Program of Russian Federation 2021–2030.

Author information

Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory of SB RAS, 134 Lermontov Street, 664033, Irkutsk, Russia

    Tatiana V. Gruzdeva

  2. Melentiev Energy Systems Institute of SB RAS, 130 Lermontov Street, 664033, Irkutsk, Russia

    Oleg V. Khamisov

Authors
  1. Tatiana V. Gruzdeva
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  2. Oleg V. Khamisov
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Corresponding author

Correspondence to Tatiana V. Gruzdeva .

Editor information

Editors and Affiliations

  1. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Nicholas N. Olenev

  2. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Yuri G. Evtushenko

  3. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  4. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  5. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Gruzdeva, T.V., Khamisov, O.V. (2021). On Search for All Roots of a System of Quadratic Equations. In: Olenev, N.N., Evtushenko, Y.G., Jaćimović, M., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2021. Lecture Notes in Computer Science(), vol 13078. Springer, Cham. https://doi.org/10.1007/978-3-030-91059-4_8

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  • DOI: https://doi.org/10.1007/978-3-030-91059-4_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-91058-7

  • Online ISBN: 978-3-030-91059-4

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