tutorials

worst-case analyses for first-order optimization methods — If you want to get familiar with performance estimation problems, you might be interested in checking this blog post, and general pedagogical ressources and tutorials (9-hour version, 3-hour version). The most introductory parts of the tutorial relies on the PEPit package (in Python, see Github, and documentation), which contains more than 100 working examples. The most advanced parts rely on symbolic computation tools (SymPy, freely available) and more advanced codes not relying on the packages.

accelerated first-order methods — we recently published a monograph on acceleration methods (with Alexandre d’Aspremont and Damien Scieur) as well as a nice continuized approach to Nesterov’s acceleration (Mathieu Even, Raphael Berthier, et al.) which received an outstanding paper award at NeurIPS 2021. We also discovered a definitive answer to the black-box complexity of large-scale smooth strongly convex minimization with Yoel Drori (in two papers: lower complexity bound and matching upper bound).

selected sets of slides —

• Perspectives on the analysis and design of optimization algorithms (slides)
• Computer-aided analyses of first-order methods (via semidefinite programming) (slides, [long version], video)
• Non-asymptotic and computer-aided analyses via potential functions (slides [long version], video)
• Computer-aided worst-case analyses for operator splitting (slides)
• A few constructive approaches to optimal first-order optimization methods for convex optimization (slides [longer versions], video [longer version])