@Article{IJNAM-20-4,
author = {Yizun, Lin and Si, Li and Zhang, Yunzhong},
title = {Convergence Rate Analysis of Accelerated Forward-Backward Algorithm with Generalized Nesterov Momentum Scheme},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2023},
volume = {20},
number = {4},
pages = {518--537},
abstract = {<p style="text-align: justify;">Nesterov’s accelerated forward-backward algorithm (AFBA) is an efficient algorithm
for solving a class of two-term convex optimization models consisting of a differentiable function
with a Lipschitz continuous gradient plus a nondifferentiable function with a closed form of its
proximity operator. It has been shown that the iterative sequence generated by AFBA with a
modified Nesterov’s momentum scheme converges to a minimizer of the objective function with
an $o
(\frac{1}{k^2})$ convergence rate in terms of the function value (FV-convergence rate) and an $o(\frac{1}{k})$ convergence rate in terms of the distance between consecutive iterates (DCI-convergence rate). In
this paper, we propose a more general momentum scheme with an introduced power parameter $ω ∈ (0, 1]$ and show that AFBA with the proposed momentum scheme converges to a minimizer
of the objective function with an $o
( \frac{1}{ k^{2ω}} )$ FV-convergence rate and an $o
(\frac{1}{k^ω})$ DCI-convergence
rate. The generality of the proposed momentum scheme provides us a variety of parameter
selections for different scenarios, which makes the resulting algorithm more flexible to achieve
better performance. We then employ AFBA with the proposed momentum scheme to solve the
smoothed hinge loss $ℓ_1$-support vector machine model. Numerical results demonstrate that the
proposed generalized momentum scheme outperforms two existing momentum schemes.</p>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2023-1022},
url = {https://global-sci.com/article/82904/convergence-rate-analysis-of-accelerated-forward-backward-algorithm-with-generalized-nesterov-momentum-scheme}
}