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The Bernstein algorithm using the modified implicit Bernstein form and its GPU parallelization using CUDA

Author

Listed:
  • P. S. Dhabe

    (Indian Institute of Technology)

  • P. S. V. Nataraj

    (Indian Institute of Technology)

Abstract

In this paper, we propose a Modified Implicit Bernstein Form (MIBF) for computing the Bernstein coefficients of a polynomial. The MIBF avoids several redundant computations in Smith’s Implicit Bernstein Form (IBF) (Smith in J Glob Optim 43:445–458, 2009). Based on the MIBF, we then propose a serial (or CPU based) Bernstein Algorithm for polynomial global optimization. On a set of test problems, the proposed Bernstein Algorithm is about 1.8 times faster than the one based on IBF in Dhabe and Nataraj (Int J Syst Assur Eng Manag, 2017). To obtain further speedups, we next propose a GPU parallel optimization algorithm based on the MIBF, and obtain speedups of up to 44 times with 97% reductions in computations over the serial version. Thus, we recommend the GPU parallel Bernstein algorithm based on the proposed MIBF form for solving polynomial global optimization problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:ijsaem:v:8:y:2017:i:4:d:10.1007_s13198-017-0673-x
    DOI: 10.1007/s13198-017-0673-x
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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. 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.
    3. 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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