Linear convergence of forward-backward accelerated algorithms without knowledge of the modulus of strong convexity

arXiv:2306.09694v2 Announce Type: replace-cross
Abstract: A significant milestone in modern gradient-based optimization was achieved with the development of Nesterov's accelerated gradient descent (NAG) method. This forward-backward technique has been further advanced with the introduction of its proximal generalization, commonly known as the fast iterative shrinkage-thresholding algorithm (FISTA), which enjoys widespread application in image science and engineering. Nonetheless, it remains unclear whether both NAG and FISTA exhibit linear convergence for strongly convex functions. Remarkably, these algorithms demonstrate convergence without requiring any …

abstract advanced algorithm algorithms arxiv convergence cs.lg cs.na development gradient introduction iterative knowledge linear math.na math.oc modern modulus optimization shrinkage stat.ml thresholding type