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 those introductory exercises. Two packages allow playing with performance estimation problems without spending too much time in the details: PESTO (in Matlab, see Github, and documentation) and PEPit (in Python, see Github, and documentation). Both packages contain more than 50 examples of applications.

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 —

  • Introduction to computer-assisted proofs in optimization and numerical analysis (upcoming)
  • 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])
  • Performance estimation toolbox (PESTO) (upcoming)