Projection-Free Optimization on Uniformly Convex Sets

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Affine Invariant Analysis of Frank-Wolfe on Strongly Convex Sets (2020, background): “H¨olderian Error Bounds on f [Kerdreux et al. 2018a; Xu et al. 2018; Rinaldi et al. 2020] or local uniform convexity of C [Kerdreux et al. 2020].”
Complexity of Linear Minimization and Projection on Some Sets (2021, background): “Faster rates can be established under additional assumptions on the properties of f or the geometry of C [41, 23, 20, 31].”
Minimization Over the Nonconvex Sparsity Constraint Using A Hybrid First-order method (2021, methodology): “In the last decades, a number of research efforts have extended the FW method to the minimization of a nonconvex objective over convex sets [29, 41].”
Linear Bandits on Uniformly Convex Sets (2021, methodology): “Note that some works recently relied on smoothness [LK19] or uniform convexity assumptions on the set in online linear learning [Hua+16; Hua+17; Mol20; KdP21b] or “online learning with a hint” [DHJ+17; Bha+20a; Bha+20b].”
A unifying framework for the analysis of projection-free first-order methods under a sufficient slope condition (2020, background): “, [29], [45]) under Hölderian error bound conditions, to interpolate between the well known O(1/k) rate for general convex objectives and the faster rates for strongly convex ones proved in [19] and [30].”