Abstract
This paper generalizes the widely used Nelder and Mead (Comput J 7:308–313, 1965) simplex algorithm to parallel processors. Unlike most previous parallelization methods, which are based on parallelizing the tasks required to compute a specific objective function given a vector of parameters, our parallel simplex algorithm uses parallelization at the parameter level. Our parallel simplex algorithm assigns to each processor a separate vector of parameters corresponding to a point on a simplex. The processors then conduct the simplex search steps for an improved point, communicate the results, and a new simplex is formed. The advantage of this method is that our algorithm is generic and can be applied, without re-writing computer code, to any optimization problem which the non-parallel Nelder–Mead is applicable. The method is also easily scalable to any degree of parallelization up to the number of parameters. In a series of Monte Carlo experiments, we show that this parallel simplex method yields computational savings in some experiments up to three times the number of processors.
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Lee, D., Wiswall, M. A Parallel Implementation of the Simplex Function Minimization Routine. Comput Econ 30, 171–187 (2007). https://doi.org/10.1007/s10614-007-9094-2
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DOI: https://doi.org/10.1007/s10614-007-9094-2