The accelerated backward-forward method achieves O(1/k²) convergence on convex composite problems and accelerated linear convergence when the smooth component is strongly convex.
SIAM Journal on Optimization 27(3), 1283–1313 (2017)
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Accelerated Backward Forward Method for Convex Optimization
The accelerated backward-forward method achieves O(1/k²) convergence on convex composite problems and accelerated linear convergence when the smooth component is strongly convex.