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In numerous applications across all science and engineering areas, there areoptimization problems where both the objective function and the constraintshave no closed-form expression or are too complex to be managed analytically,that they can only be evaluated through experiments. To address such issues, wedesign a global optimization technique for problems with black-box objectiveand constraints. Assuming Lipschitz continuity of the cost and constraintfunctions, a Set Membership framework is adopted to build a surrogate model ofthe optimization program, that is used for exploitation and explorationroutines. The resulting algorithm, named Set Membership Global OptimizationWith Black-Box Constraints (SMGO-$\Delta$), features one tunable riskparameter, which the user can intuitively adjust to trade-off safety,exploitation, and exploration. The theoretical properties of the algorithm arederived, and the optimization performance is compared with representativetechniques from the literature in several benchmarks. Lastly, it is tested andcompared with constrained Bayesian optimization in a case study pertaining tomodel predictive control tuning for a servomechanism with disturbances andplant uncertainties, addressing practically-motivated task-level constraints.

SMGO-$\Delta$: Balancing Caution and Reward in Global Optimization with Black-Box Constraints