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A parallel Bernstein algorithm for global optimization based on the implicit Bernstein form

Author

Listed:
  • P. S. Dhabe

    (Indian Institute of Technology Bombay)

  • P. S. V. Nataraj

    (Indian Institute of Technology Bombay)

Abstract

In this paper, we first present a serial Bernstein algorithm for polynomial global optimization based on the Implicit Bernstein Form (IBF) (Smith in J Glob Optim 43:445–458, 2009). The serial Bernstein algorithm based on IBF needs less computations and memory than the conventional Bernstein algorithm and its variants. To accelerate further the Bernstein algorithm based on the IBF, we next propose a parallel version for GPU computing using Compute Unified Device Architecture. With the parallel version, the exponential time-complexity of the serial algorithm reduces to linear time-complexity. We compare the performance of both the versions on a set of 12 test problems, and find that the parallel version is up to 26 times faster and takes 96% less time than the serial one. Based on these findings, we suggest the use of the parallel version of the Bernstein algorithm based on IBF in polynomial global optimization.

Suggested Citation

  • P. S. Dhabe & P. S. V. Nataraj, 2017. "A parallel Bernstein algorithm for global optimization based on the implicit Bernstein form," 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. 8(2), pages 1654-1671, November.
    • Handle: RePEc:spr:ijsaem:v:8:y:2017:i:2:d:10.1007_s13198-017-0639-z
    DOI: 10.1007/s13198-017-0639-z
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. Titi, Jihad & Garloff, Jürgen, 2019. "Matrix methods for the tensorial Bernstein form," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 254-271.
    2. P. S. Dhabe & P. S. V. Nataraj, 2017. "The Bernstein algorithm using the modified implicit Bernstein form and its GPU parallelization using CUDA," 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. 8(4), pages 826-841, December.

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