A modified proximal bundle method with a fixed absolute accuracy null-step test is shown via Frank-Wolfe duality to have O(ε^{-4/5} log^{2/5}(1/ε)) iteration complexity.
Alexander, The width and diameter of a simplex, Geometriae Dedicata, 6 (1977), pp
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An Absolute-Error Proximal Bundle Method through the Lens of Frank-Wolf
A modified proximal bundle method with a fixed absolute accuracy null-step test is shown via Frank-Wolfe duality to have O(ε^{-4/5} log^{2/5}(1/ε)) iteration complexity.