APAPC integrates Nesterov acceleration into primal-dual forward-backward schemes by exploiting dual strong convexity to achieve optimal sublinear and accelerated linear convergence rates.
arXiv:2601.15398 (2026)
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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.
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A Nesterov-Accelerated Primal-Dual Splitting Algorithm for Convex Nonsmooth Optimization
APAPC integrates Nesterov acceleration into primal-dual forward-backward schemes by exploiting dual strong convexity to achieve optimal sublinear and accelerated linear convergence rates.
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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.