Abstract: This research introduces the direct-search algorithm StoMADS for unconstrained stochastic blackbox optimization and extends it to problems involving general constraints by introducing StoMADS-PB. Both methods use estimates because of the unavailability of the objective and constraint functions values which are provided by a noisy blackbox, i.e., they can only be computed with random noise whose distribution is unknown. StoMADS-PB which aggregates constraint violations into a single constraint violation function, introduces probabilistic bounds for the violation. All the estimates and bounds are required to be accurate and reliable with high, but fixed, probabilities. While both algorithms accept new points using sufficient decrease conditions, StoMADS-PB allows in particular intermediate infeasible solutions and imposes a threshold on the probabilistic bounds. Using Clarke nonsmooth calculus and martingale theory, Clarke stationarity convergence results for the objective and the violation function are derived with probability one. By generalizing the algorithmic framework of StoMADS, a broad class of stochastic directional direct-search (SDDS) methods is also proposed, with expected complexity analysis using an existing supermartingale-based framework.
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Meeting ID: 866 714 245 // Participant Code: 6398