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Projection free methods on product domains

Author

Listed:
  • Immanuel Bomze

    (Universität Wien)

  • Francesco Rinaldi

    (University of Padua)

  • Damiano Zeffiro

    (University of Padua)

Abstract

Projection-free block-coordinate methods avoid high computational cost per iteration, and at the same time exploit the particular problem structure of product domains. Frank–Wolfe-like approaches rank among the most popular ones of this type. However, as observed in the literature, there was a gap between the classical Frank–Wolfe theory and the block-coordinate case, with no guarantees of linear convergence rates even for strongly convex objectives in the latter. Moreover, most of previous research concentrated on convex objectives. This study now deals also with the non-convex case and reduces above-mentioned theory gap, in combining a new, fully developed convergence theory with novel active set identification results which ensure that inherent sparsity of solutions can be exploited in an efficient way. Preliminary numerical experiments seem to justify our approach and also show promising results for obtaining global solutions in the non-convex case.

Suggested Citation

  • Immanuel Bomze & Francesco Rinaldi & Damiano Zeffiro, 2025. "Projection free methods on product domains," Computational Optimization and Applications, Springer, vol. 91(2), pages 511-540, June.
    • Handle: RePEc:spr:coopap:v:91:y:2025:i:2:d:10.1007_s10589-024-00585-5
    DOI: 10.1007/s10589-024-00585-5
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    References listed on IDEAS

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    1. Hédy Attouch & Jérôme Bolte & Patrick Redont & Antoine Soubeyran, 2010. "Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 438-457, May.
    2. NESTEROV, Yurii, 2012. "Efficiency of coordinate descent methods on huge-scale optimization problems," LIDAM Reprints CORE 2511, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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.
    4. 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.
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