Conditional Gradient Methods

From Core Principles to AI Applications

By: Gabor Braun, Alejandro Carderera, Cyrille W. Combettes, Hamed Hassani, Amin Karbasi

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Paperback | 15 March 2026

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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 unites deep theoretical insights with practical considerations, guiding readers through the foundations of constrained optimization and into cutting-edge territory, including stochastic, online, and distributed settings. With a clear narrative, rigorous proofs, and illuminating illustrations, the book demystifies adaptive variants, away-steps, and the nuances of dealing with structured convex sets. A FrankWolfe.jl Julia package that implements most of the algorithms in the book is available on a supplementary website.

Industry Reviews

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, Princeton University ""Conditional Gradient Methods is a thorough and accessible guide to one of the most versatile families of optimization algorithms. The book 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, their 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, INRIA

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