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A GPU parallel Bernstein algorithm for polynomial global optimization

Author

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  • Priyadarshan Dhabe

    (Indian Institute of Technology Bombay)

  • P. S. V. Nataraj

    (Indian Institute of Technology Bombay)

Abstract

We come up with a graphics processing unit (GPU) parallel Bernstein algorithm (BA) aimed at global optimization of multi-variate real polynomials (Garloff in Interval Comput 2:164–168, 1993). We first propose parallel algorithms for (a) computing the multi-index set associated with the Bernstein coefficients (BCs), (b) computing the initial set of BCs using the Matrix method (Ray and Nataraj in Reliab Comput 17(1):40–71, 2012), (c) finding the minimum BC from a given set of BCs, and (d) finding the BCs of the child patches from the parent patch. We then incorporate the above components into the proposed parallel Bernstein algorithm. All the parallel algorithms are programmed for GPU accelerating devices through compute unified device architecture. We compared performance of serial and GPU parallel BA using a test suite of 8 multivariate examples. For the test examples, the proposed parallel algorithm is found 30 times faster as compared to serial one, and needs 96% less time.

Suggested Citation

  • Priyadarshan Dhabe & P. S. V. Nataraj, 2020. "A GPU parallel Bernstein algorithm for polynomial global optimization," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 11(1), pages 21-44, February.
    • Handle: RePEc:spr:ijsaem:v:11:y:2020:i:1:d:10.1007_s13198-019-00922-6
    DOI: 10.1007/s13198-019-00922-6
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    References listed on IDEAS

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    1. P. Nataraj & M. Arounassalame, 2011. "Constrained global optimization of multivariate polynomials using Bernstein branch and prune algorithm," Journal of Global Optimization, Springer, vol. 49(2), pages 185-212, February.
    2. Salhi, S. & Queen, N. M., 2004. "A hybrid algorithm for identifying global and local minima when optimizing functions with many minima," European Journal of Operational Research, Elsevier, vol. 155(1), pages 51-67, May.
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