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The Multistart Coordinate Search Filter (MCSFilter) method is an optimization method able to find all minimizers (local and global) of a nonlinear and nonconvex problem. Reducing the time to find such minimizers may be of uttermost importance, specially in real-world applications, whether for economical reasons or due to other constrains of the processes under the control of optimization methods. In this paper, a first attempt to come up with a parallel version of the MCSFilter, tailored to multi-core machines, is described and discussed. Although the evaluation results indicate that this first parallel version ensures a moderate speedup, adequate to desktop-level systems, this work paves the way for increasingly efficient versions to be developed futurely.