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

P. S. Dhabe () and P. S. V. Nataraj ()
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P. S. Dhabe: Indian Institute of Technology
P. S. V. Nataraj: Indian Institute of Technology

International Journal of System Assurance Engineering and Management, 2017, vol. 8, issue 4, No 13, 826-841

Abstract: 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.

Keywords: Bernstein algorithm; Bernstein polynomials; Global optimization; GPU computing; Parallel computing; Polynomial optimization (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13198-017-0673-x

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