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Frank–Wolfe and friends: a journey into projection-free first-order optimization methods

Author

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  • Immanuel M. Bomze

    (Universität Wien)

  • Francesco Rinaldi

    (Università di Padova)

  • Damiano Zeffiro

    (Università di Padova)

Abstract

Invented some 65 years ago in a seminal paper by Marguerite Straus-Frank and Philip Wolfe, the Frank–Wolfe method recently enjoys a remarkable revival, fuelled by the need of fast and reliable first-order optimization methods in Data Science and other relevant application areas. This review tries to explain the success of this approach by illustrating versatility and applicability in a wide range of contexts, combined with an account on recent progress in variants, improving on both the speed and efficiency of this surprisingly simple principle of first-order optimization.

Suggested Citation

  • Immanuel M. Bomze & Francesco Rinaldi & Damiano Zeffiro, 2021. "Frank–Wolfe and friends: a journey into projection-free first-order optimization methods," 4OR, Springer, vol. 19(3), pages 313-345, September.
    • Handle: RePEc:spr:aqjoor:v:19:y:2021:i:3:d:10.1007_s10288-021-00493-y
    DOI: 10.1007/s10288-021-00493-y
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    References listed on IDEAS

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    Cited by:

    1. James Chok & Geoffrey M. Vasil, 2023. "Convex optimization over a probability simplex," Papers 2305.09046, arXiv.org.
    2. Bomze, Immanuel M. & Gabl, Markus & Maggioni, Francesca & Pflug, Georg Ch., 2022. "Two-stage stochastic standard quadratic optimization," European Journal of Operational Research, Elsevier, vol. 299(1), pages 21-34.
    3. Francesco Rinaldi & Damiano Zeffiro, 2023. "Avoiding bad steps in Frank-Wolfe variants," Computational Optimization and Applications, Springer, vol. 84(1), pages 225-264, January.

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