Year: 2026
Type: article
Abstract: We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is assumed unknown, without resorting to line search procedures. The sequence generated by this method converges weakly to a minimizer of the objective function, and the function values converge at a fast rate of $$\mathcal {O}\left( \frac{1}{k^2} \right) $$ O 1 k 2 . Moreover, if the objective function is strongly convex, the function values converge at a linear rate $$\mathcal {O}\left( \frac{1}{k^2}(1-\rho )^k \right) $$ O 1 k 2 ( 1 - ρ ) k , with $$\rho =\mathcal {O}\left( \frac{\mu }{L} \right) $$ ρ = O μ L , without knowledge of the strong convexity parameter.
Authors: Zepeng Wang, Juan Peypouquet
Institution: University of Groningen
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W7117248346