SMGO-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si75.svg"><mml:mrow><mml:mi mathvariant="normal">?</mml:mi></mml:mrow></mml:math>: Balancing caution and reward in global optimization with black-box constraints

In numerous applications across all science and engineering areas, there are optimization problems where both the objective function constraints have no closed-form expression or too complex to be managed analytically, so that they can only evaluated through experiments. To address such issues, we design a global technique for with black-box constraints. Assuming Lipschitz continuity of cost constraint functions, Set Membership framework is adopted build surrogate model program, used exploitation exploration routines. The resulting algorithm, named Global Optimization (SMGO-?), features one tunable risk parameter, which user intuitively adjust trade-off safety, exploitation, exploration. theoretical properties algorithm derived, performance compared representative techniques from literature in several benchmarks. An extension uncertain cost/constraint outcomes presented, too, as well computational aspects. Lastly, approach tested constrained Bayesian case study pertaining predictive control tuning servomechanism disturbances plant uncertainties, addressing practically-motivated task-level