Some contributions to global optimization.

Summary This thesis is concerned with the sequential optimization problem of an unknown function defined on a continuous and bounded set. This type of problem appears in particular in the design of complex systems, when one seeks to optimize the result of numerical simulations or more simply when the function that one wishes to optimize does not present any form of obvious regularity like linearity or convexity. In a first step, we focus on the particular case of lipschitzian functions. We introduce two new strategies aiming at optimizing any function of known and unknown Lipschitz coefficient. Then, by introducing different regularity measures, we formulate and obtain consistency results for these methods as well as convergence speeds on their approximation errors. In a second part, we propose to explore the domain of binary scheduling in order to develop optimization strategies for non-regular functions. By observing that learning the scheduling rule induced by the unknown function allows the systematic identification of its optimum, we make the link between scheduling theory and optimization theory, which allows us to develop new methods based on the choice of any scheduling technique and to formulate different convergence results for the optimization of non-regular functions. Finally, the optimization strategies developed during the thesis are compared to existing state-of-the-art methods on calibration problems of learning systems as well as on synthetic problems frequently encountered in the field of global optimization.