  This work introduces StoMADS, a stochastic variant of the mesh adaptive
direct-search (MADS) algorithm originally developed for deterministic blackbox
optimization. StoMADS considers the unconstrained optimization of an objective
function f whose values can be computed only through a blackbox corrupted by
some random noise following an unknown distribution. The proposed method is
based on an algorithmic framework similar to that of MADS and uses random
estimates of function values obtained from stochastic observations since the
exact deterministic computable version of f is not available. Such estimates
are required to be accurate with a sufficiently large but fixed probability and
satisfy a variance condition. The ability of the proposed algorithm to generate
an asymptotically dense set of search directions is then exploited to show
convergence to a Clarke stationary point of f with probability one, using
martingale theory.
