This work introduces STOMADS, a stochastic variant of the Mesh Adaptive Direct Search (MADS) algorithm designed for deterministic blackbox optimization. STOMADS considers the constrained optimization of an (unknown) objective function f whose values can only be computed with some random noise of an unknown distribution. The proposed algorithm uses an algorithmic concept similar to that of MADS and utilizes random estimates of true function values obtained from their stochastic observations to ensure improvements 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 certain variance condition. The ability of the proposed algorithm to generate an asymptotically dense set of search directions is then exploited to show that it converges to a Clarke stationary point with probability one, with the help of martingale theory.
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