Optimisation non différentiable et optimisation stochastique : de la théorie aux applications

This document is devoted to theoretical and practical aspects of two subelds of the mathematical programming, namely nonsmooth optimization and stochastic programming. In general, real-life stochastic programming models give rise to large-scale optimization problems that can only be solved with the help of decomposition techniques and specialized algorithms. Invariably, techniques such as Benders decomposition, Lagrangian relaxation, two-stage or multistage decomposition yield objective functions that are not only nonsmooth but also difficult to evaluate. For this reason, efficient nonsmooth optimization methods must come into play. This document highlights some of my contributions to these key subfields for decision-making in real-life optimization problems, such as those coming from the industry of energy