Optimization takes place in many IFPEN applications: for instance estimation of parameters of numerical models from experimental data in geosciences or for engine calibration. These optimization problems consist in minimizing a complex function, expensive to estimate, and for which derivatives are often not available. Moreover, additional difficulties arise with the introduction of nonlinear constraints and even several objectives to be minimized. In this thesis, we developed the SQA method (Sequential Quadratic Approximation), an extension of a derivative-free optimization method proposed by M.J.D Powell for optimization with constraints with known or unknown derivatives. This method consists in solving optimization sub-problems based on local quadratic interpolation models of objective function and derivative-free constraints built with a limited number of function evaluations. If the solution of this sub-problem does not progress toward a solution of the original problem, new simulations are performed to try to improve the model quality. Numerical results on benchmarks show that SQA is an effective method for constrained derivative-free optimization. Finally, SQA has been tested with success on two industrial applications in reservoir engineering and in engine calibration. An other problem studied in this thesis is multi-objective minimization under constraints. The MO-CMA-ES method (Multi-Objective - Covariance Matrix Adaptation - Evolution Strategy) adapted to take into account constraints has been successful to determine different compromises for an engine calibration application.
