Annals of Mathematical Sciences and Applications

Volume 8 (2023)

Number 2

Special issue dedicated to Anthony To-Ming Lau on his 80th birthday

Guest Editors: Xiaolong Qin, Ngai-Ching Wong and Jen-Chih Yao

Refinements of some convergence results of the gradient-projection algorithm

Pages: 347 – 363

DOI: https://dx.doi.org/10.4310/AMSA.2023.v8.n2.a8

Author

Hong-Kun Xu (School of Science, Hangzhou Dianzi University, Hangzhou, China)

Abstract

In this note we refine some of the results of [$\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=2818926}{18}$] on the gradient-projection algorithm in the infinite-dimensional Hilbert space setting by weakening the conditions imposed on the choices of the parameters in [$\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=2818926}{18}$, Theorems 4.2, 4.3 and 5.2]. In addition, we also show that the relaxed gradient-projection algorithm has a sublinear rate of convergence.

Keywords

gradient-projection, fixed point algorithm, averaged mapping, viscosity approximation method

2010 Mathematics Subject Classification

Primary 47Hxx, 90C25. Secondary 47H09, 49J40.

Received 31 May 2023

Accepted 24 June 2023

Published 26 July 2023