Winner
Eitan Levin (Applied and Computational Mathematics, California Institute of Technology, USA) for the paper titled "The effect of smooth parametrizations on nonconvex optimization landscapes" jointly authored with Joe Kileel and Nicolas Boumal.
Citation
This paper introduces a novel framework for analyzing relationships between optimization landscapes in nonconvex settings by utilizing smooth parametrizations, or "lifts," that map one optimization problem onto another. The authors systematically investigate how desirable properties, such as local minima and critical points in one problem, are preserved when mapped to another problem through these lifts. This framework is applied to a wide range of optimization problems, including low-rank matrix and tensor optimization, semidefinite programming, and training neural networks, revealing new insights into the structure and behavior of these problems. A key contribution is the identification of conditions under which lifts preserve various optimization properties, such as ensuring that local minima and stationary points in one problem correspond to similar points in the mapped problem. The authors demonstrate that these results generalize and unify many previously known results, providing a more comprehensive understanding of how optimization landscapes behave under parametrization.
Additionally, the paper explores the construction of lifts using fiber products and presents a detailed analysis of specific lifts, including the Burer-Monteiro lift for smooth semidefinite programs and lifts for low-rank matrices and tensors. The work sheds light on critical concepts in nonconvex optimization, such as benign nonconvexity, the strict saddle property, and hidden convexity, offering a reusable proof technique applicable across a broad range of problems. This paper stands out for its conceptual clarity and technical depth, addressing fundamental questions that have not been previously formulated in the optimization community. The framework developed has the potential to inspire significant follow-up research, both theoretical and algorithmic, making it a deserving candidate for this prize.
Second Place
Liwei Jiang (Georgia Institute of Technology) for the paper "Asymptotic Normality and Optimality in Nonsmooth Stochastic Approximation" jointly authored with Damek Davis and Dmitriy Drusvyatskiy.
Honorable Mention
Zikai Xiong (Massachusetts Institute of Technology) for the paper "Computational Guarantees for Restarted PDHG for LP Based on 'Limiting Error Ratios' and LP Sharpness" jointly authored with Robert M. Freund.
Honorable Mention
Sanyou Mei (University of Minnesota) for the paper "Accelerated First-Order Methods for Convex Optimization with Locally Lipschitz Continuous Gradient" jointly authored with Zhaosong Lu.
Prize committee
Necdet Serhat Aybat, Albert Berahas, Georgina Hall, Robert Hildebrand (Chair), Aida Khajavirad, Weijun Xie