Book
A SIAM monograph on Frank-Wolfe algorithms for constrained optimization, machine learning, and large-scale data science.
MOS-SIAM Series on Optimization · 2025
G. Braun, A. Carderera, C.W. Combettes, H. Hassani, A. Karbasi, A. Mokhtari, S. Pokutta
Conditional Gradient Methods: From Core Principles to AI Applications offers a definitive and modern treatment of one of the most elegant and versatile algorithmic families in optimization: the Frank–Wolfe method and its many variants. Originally proposed in the 1950s, these projection-free techniques have seen a powerful resurgence, now playing a central role in machine learning, signal processing, and large-scale data science.
This comprehensive monograph guides readers through the foundations of constrained optimization and into cutting-edge territory — including stochastic, online, and distributed settings — by uniting deep theoretical insights with practical considerations. It uses a clear narrative, rigorous proofs, and illuminating illustrations to demystify adaptive variants, away-steps, and the nuances of dealing with structured convex sets.
Most of the algorithms in the book are implemented in the FrankWolfe.jl Julia package.
Endorsements
“Conditional gradient algorithms have become an essential part of the algorithmic toolbox in machine learning, signal processing, and related fields. This monograph offers a comprehensive review of both classical results and recent generalizations, including extensions to large-scale settings. The presentation is notably clear, featuring illustrations, detailed proofs, and application examples. It will serve as an important reference for graduate students and researchers in data science.”
— Francis Bach, INRIA
“This book is a thorough and accessible guide to one of the most versatile families of optimization algorithms. It traces the rich history of the conditional gradient algorithm and explores its modern advancements, offering a valuable resource for both experts and newcomers. With clear explanations of the algorithms, analysis, and practical applications, the authors provide a go-to reference for anyone tackling constrained optimization problems. This book is sure to inspire fresh ideas and drive advancements in the field.”
— Elad Hazan, Princeton University
Audience
This book is intended for optimization researchers and theorists, machine learning methodologists, and algorithm designers. Graduate students in those areas will also find it of interest.