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

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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.

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Authors and Affiliations

  1. Systems and Control Engineering Group, Indian Institute of Technology, Bombay, 400076, India

    P. S. Dhabe & P. S. V. Nataraj

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  1. P. S. Dhabe
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  2. P. S. V. Nataraj
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Correspondence to P. S. V. Nataraj.

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Dhabe, P.S., Nataraj, P.S.V. The Bernstein algorithm using the modified implicit Bernstein form and its GPU parallelization using CUDA. Int J Syst Assur Eng Manag 8, 826–841 (2017). https://doi.org/10.1007/s13198-017-0673-x

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  • DOI: https://doi.org/10.1007/s13198-017-0673-x

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