Informations on my HdR
Title
Variational-analysis look at combinatorial optimization
and other selected topics in optimization
Committee
- Alexandre d'Aspremont, ENS Ulm
- Jérome Bolte, Toulouse School of Economics
- Gérard Cornuéjols, Carnegie Mellon University
- Jean Lasserre, LAAS-CNRS
- Nabil Layaida, Inria
- Yurii Nesterov, Université de Louvain (Belgique)
- Michael Overton, Courant Institute of Mathematical Sciences, NYU
Defense
Thursday January 26, 2017, at 14:30, at the amphi of the Maison Jean Kunztmann
Have a look the slides of the presentation. Fun story: we met a Nobel Prize Winner during the little celebration following the defense.
Summary of the document
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.