2024 Lagrange Prize Citation

Jérôme Bolte and Edouard Pauwels

The Lagrange Prize in Continuous Optimization 2024 is presented to Jérôme Bolte and Edouard Pauwels for their paper "Conservative set valued fields, automatic differentiation, stochastic gradient methods and deep learning", Mathematical Programming, Vol. 188, 2021.
Bolte and Pauwels model the algorithmic differentiation operation via new variational objects called conservative set valued fields. They also conduct the convergence analysis to critical points for nonsmooth stochastic first-order methods. Their paper combines techniques from several fields including non-smooth analysis, firstorder stochastic approximation, machine learning, and algorithmic differentiation, with a central role played by o-minimal geometry. Bolte and Pauwels thus provide a remarkable theoretical and algorithmic contribution to the field of continuous optimization.