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Fast Convergence of Frank-Wolfe Algorithms on Polytopes

Author

Listed:
  • Elias Wirth

    (Technical University of Berlin, 10623 Berlin, Germany)

  • Javier Peña

    (Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • Sebastian Pokutta

    (Technical University of Berlin, 10623 Berlin, Germany; and Zuse Institute Berlin, 14195 Berlin, Germany)

Abstract

We provide a template to derive affine-invariant convergence rates for the following popular versions of the Frank-Wolfe algorithm on polytopes: vanilla Frank-Wolfe, Frank-Wolfe with away steps, Frank-Wolfe with blended pairwise steps, and Frank-Wolfe with in-face directions. Our template shows how the convergence rates follow from two affine-invariant properties of the problem, namely, error bound and extended curvature . These properties depend solely on the polytope and objective function but not on any affine-dependent object like norms. For each one of the above algorithms, we derive rates of convergence ranging from sublinear to linear depending on the degree of the error bound.

Suggested Citation

  • Elias Wirth & Javier Peña & Sebastian Pokutta, 2026. "Fast Convergence of Frank-Wolfe Algorithms on Polytopes," Mathematics of Operations Research, INFORMS, vol. 51(2), pages 1463-1485, May.
    • Handle: RePEc:inm:ormoor:v:51:y:2026:i:2:p:1463-1485
    DOI: 10.1287/moor.2024.0580
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