Optimization of a computationally expensive simulator with quantitative and qualitative inputs

In this thesis, expensive mixed problems are addressed through Gaussian processes where discrete variables are relaxed into continuous latent variables. The continuous space is more easily exploited by classical Bayesian optimization techniques than would be a mixed space. The discrete variables are recovered either after the continuous optimization or simultaneously with an additional constraint of continuous-discrete compatibility which is treated with augmented Lagrangians. Several possible implementations of these mixed Bayesian optimizers are compared. In particular, the reformulation of the problem with continuous latent variables is put in competition with research working directly in the mixed space. Among the algorithms involving latent variables and an augmented Lagrangian, particular attention is devoted to Lagrangian multipliers for which local and global estimation techniques are studied. Comparisons are based on repeated optimization of three analytical functions and on a mechanical application concerning the design of a beam. An additional study for the application of a proposed mixed optimization strategy in the field of mixed self-calibration is made. This analysis is inspired by a radionuclide quantification application, which defines a specific inverse function requiring the study of its multiple properties in the continuous scenario. A proposal of different deterministic and Bayesian strategies has been made for a complete definition in a mixed variable context.