Prize History

Citation

The 2024 Lagrange Prize in Continuous Optimization is awarded to Jérôme Bolte and Edouard Pauwels for their paper Conservative set valued fields, automatic differentiation, stochastic gradient methods and deep learning, published in Mathematical Programming in 2020. Bolte and Pauwels introduce generalized derivatives called conservative fields and provide variational formulas for non-smooth automatic differentiation oracles with applications in stochastic gradient methods.

Selection Committee

• Renata Sotirov (Chair)
• Michael Friedlander
• Roland Herzog
• Stefan Wild

Citation

The 2021 Lagrange Prize is awarded to Léon Bottou, Frank E. Curtis, and Jorge Nocedal for their paper, "Optimization Methods for Large-Scale Machine Learning", SIAM Review 60(2), 2018, which provides a foundational and insightful review of optimization methods for large-scale machine learning, including a new perspective for the simultaneous consideration of noise reduction and ill-conditioning and the foundations and analysis of second-order stochastic optimization methods for machine-learning.

Selection Committee

• Sven Leyffer (Chair)
• Xiaojun Chen
• Etienne de Klerk
• Philip Gill

Citation

The 2018 Lagrange Prize is awarded to Francis Bach, Nicolas Le Roux, and Mark Schmidt for their paper, "Minimizing finite sums with the stochastic average gradient" (NIPS, 2012; Mathematical Programming, 2017).

This paper is the first in a series of significant advances in the design and analysis of stochastic gradient methods applied to finite-sum problems. In particular, it establishes that in this setting, the proposed variant of a stochastic gradient method achieves a linear convergence rate. This novel approach has resulted in a surge of interest in variance reduction methods that achieve superior performance compared to other first-order methods. A wide range of applications benefit from this methodology, including linear least squares, principal component analysis, and L1-regularization problems. In summary, this work represents a paradigm shift in theoretical analysis of stochastic methods applied to finite-sum optimization problems.

Selection Committee

• Katya Scheinberg (Chair)
• Etienne de Klerk
• Philip Gill
• Andreas Griewank

Citation

The 2015 Lagrange Prize is awarded to Andrew R. Conn, Katya Scheinberg, and Luis Nunes Vicente for their paper "Introduction to Derivative-Free Optimization", MPS-SIAM Series on Optimization, SIAM, 2009.

This monograph represents a significant contribution in understanding the formulation of surrogate models, the construction of derivative free optimization (DFO) algorithms, and their convergence properties. It includes a groundbreaking trust region framework for convergence that has made DFO both principled and practical. A large number of key optimization studies have used these results substantively in both practical and conceptual ways. This work has not only influenced new DFO algorithms; its results have also enabled the solution of numerous optimization applications in science and engineering. A small sampling of the direct impact of their work is seen in aerospace engineering, urban transport systems, adaptive meshing for partial differential equations, and groundwater remediation.

Selection Committee

• Mihai Anitescu (Chair)
• Kurt M. Anstreicher
• Lorenz Biegler
• Werner Roemisch

Citation

The 2012 Lagrange Prize is awarded to Emmanuel J. Candès and Benjamin Recht for their paper, "Exact matrix completion via convex optimization", Foundations of Computational Mathematics 9 (2009), 717-772.

The paper of Candès and Recht was selected because of its exposition excellence, the current importance of the topic and the impressive number of citations in three years. It also opens Semidefinite Optimization to a fascinating new field of applications and introduces a very clever mathematical approach for proving probabilistic tractability of certain NP hard problems.

Selection Committee

• Tamas Terlaky (Chair)
• Kurt M. Anstreicher
• Donald Goldfarb

Selection Committee

• Adrian S. Lewis (Chair)
• Jorge J. More
• Philippe L. Toint
• Margaret H. Wright
• Thomas M. Liebling

Selection Committee

• Michael J. Todd (Chair)
• John E. Dennis Jr.
• Nicholas I. Gould
• Adrian S. Lewis

Selection Committee

• C. Tim Kelley
• Claude Lemarechal
• Michael J. Todd
• Stephen J. Wright

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