DOI: 10.24193/fpt-ro.2024.2.13

Authors: Liya Liu, Adrian Petrușel, Xiaolong Qin and Jen-Chih Yao

Abstract: We consider a convex constrained optimization problem composed in part of finding fixed points of nonexpansive mappings and in part of solving a minimization problem. Two broadcast incremental algorithms are proposed to solve it, in the spirit of the steepest-descent method and Mann’s iterative method. Under certain mild assumptions, the norm convergence of our suggested algorithms is established in the framework of real Hilbert spaces. Finally, numerical experiments on a peer to peer storage system are implemented to illustrate the performance of our algorithm.

Key Words and Phrases: Convex minimization problem, steepest decent method, nonexpansive mapping, convergence result, peer to peer storage system.

2010 Mathematics Subject Classification: 47H05, 47J25, 47H10, 65J15.

Published on-line: June 15th, 2024.

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