A GPU Parallel Bernstein Algorithm for Polynomial Global Optimization.

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.