Strong convergence of an inertial extrapolation method for a split system of minimization problems

Demonstratio mathematica

article

Anteneh Getachew Gebrie¹  Rabian Wangkeeree² 

[1] Department of Mathematics, Debre Berhan University;Department of Mathematics, Naresuan University

关键词: minimization problem;    Moreau-Yosida approximate;    inertial term;    strong convergence;   

DOI  :  10.1515/dema-2020-0025

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

In this article, we propose an inertial extrapolation-type algorithm for solving split system of minimization problems: finding a common minimizer point of a finite family of proper, lower semicontinuous convex functions and whose image under a linear transformation is also common minimizer point of another finite family of proper, lower semicontinuous convex functions. The strong convergence theorem is given in such a way that the step sizes of our algorithm are selected without the need for any prior information about the operator norm. The results obtained in this article improve and extend many recent ones in the literature. Finally, we give one numerical example to demonstrate the efficiency and implementation of our proposed algorithm.

【 授权许可】

CC BY