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GPU-Based Acceleration of the Rao Optimization Algorithms: Application to the Solution of Large Systems of Nonlinear Equations

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Intelligent Data Engineering and Automated Learning – IDEAL 2023 (IDEAL 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14404))

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Abstract

In this paper, parallel GPU-based versions of the three Rao metaphor-less optimization algorithms are proposed and used to solve large-scale nonlinear equation systems, which are hard to solve with traditional numerical methods, particularly as the size of the systems get bigger. The parallel implementations of the Rao algorithms were performed in Julia and tested on a high-performance GeForce RTX 3090 GPU with 10 496 CUDA cores and 24 GB of GDDR6X VRAM using a set of challenging scalable systems of nonlinear equations. The computational experiments carried out demonstrated the efficiency of the proposed GPU-accelerated versions of the Rao optimization algorithms, with average speedups ranging from 57.10\(\times \) to 315.12\(\times \) for the set of test problems considered in this study.

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Acknowledgements

The authors would like to thank Emiliano Gonçalves for providing access to the GPU hardware used in the computational experiments.

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Authors and Affiliations

  1. Doctoral Program in Informatics Engineering, University of Madeira, Funchal, Madeira Is., Portugal

    Bruno Silva

  2. Regional Secretariat for Education, Science and Technology, Regional Government of Madeira, Funchal, Portugal

    Bruno Silva

  3. Faculty of Exact Sciences and Engineering, University of Madeira, 9020-105, Funchal, Madeira Is., Portugal

    Luiz Guerreiro Lopes

Authors
  1. Bruno Silva
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  2. Luiz Guerreiro Lopes
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Corresponding author

Correspondence to Luiz Guerreiro Lopes .

Editor information

Editors and Affiliations

  1. University of Évora, Évora, Portugal

    Paulo Quaresma

  2. Technical University of Madrid, Madrid, Spain

    David Camacho

  3. University of Manchester, Manchester, UK

    Hujun Yin

  4. University of Évora, Évora, Portugal

    Teresa Gonçalves

  5. Polytechnic University of Valencia, Valencia, Spain

    Vicente Julian

  6. University of Huelva, Huelva, Spain

    Antonio J. Tallón-Ballesteros

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Silva, B., Lopes, L.G. (2023). GPU-Based Acceleration of the Rao Optimization Algorithms: Application to the Solution of Large Systems of Nonlinear Equations. In: Quaresma, P., Camacho, D., Yin, H., Gonçalves, T., Julian, V., Tallón-Ballesteros, A.J. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2023. IDEAL 2023. Lecture Notes in Computer Science, vol 14404. Springer, Cham. https://doi.org/10.1007/978-3-031-48232-8_11

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  • DOI: https://doi.org/10.1007/978-3-031-48232-8_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-48231-1

  • Online ISBN: 978-3-031-48232-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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