Refinements of some convergence results of the gradient-projection algorithm

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.

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Dedicated to Professor Anthony To-Ming Lau on the occasion of his 80th birthday

Received 31 May 2023

Accepted 24 June 2023

Published 26 July 2023