For convex (H0,H1)-smooth objectives, restarted accelerated gradient methods achieve O(sqrt(H0 R^2/eps)+sqrt(H1 R^2) log(F0/eps)) iterations, and accelerated coordinate variants pay a standard factor d or use importance sampling.
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A Few Accelerated Algorithms for Convex Optimization under $(H_0,H_1)$-Smoothness
For convex (H0,H1)-smooth objectives, restarted accelerated gradient methods achieve O(sqrt(H0 R^2/eps)+sqrt(H1 R^2) log(F0/eps)) iterations, and accelerated coordinate variants pay a standard factor d or use importance sampling.