Variational-analysis look at combinatorial optimization, and other selected topics in optimization

This document provides a global view on my research on mathematical optimization. Over the last 10 years, I have worked on several theoretical, algorithmic, and computational topics in optimization, driven by problems from others domains or real-life applications. I choose to focus here on a balanced set of self-contained results that are quite representative of my research approach, while illustrating different facets and particularities of my contributions. I put an emphasis on four of my main contributions: (i) semidefinite relaxations of combinatorial optimization problems, (ii) nonsmooth optimization algorithms for energy optimization, (iii) cut-generating functions in discrete optimization, and (iv) variational analysis of alternating projections. A final section briefly puts the results in perspective and discusses future research directions