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Parallel proximal method of solving split system of fixed point set constraint minimization problems

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

The purpose of this paper is to introduce iterative algorithm solving split system of fixed point set constraint minimization problem given as a task of finding a fixed point \(\bar{x}\) of a strictly pseudocontractive mapping and is also a common minimizer point of finite family of proper, lower semicontinuous convex functions and whose image \(A(\bar{x})\) under a bounded linear operator A is also common minimizer point of another finite family of proper, lower semicontinuous convex functions. Our algorithm is designed by introducing a setting that will allow us avoid the necessity of prior knowledge of the operator norm to determine the step sizes. Some applications and numerical experiment is given to analyse the efficiency of our algorithm.

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Acknowledgements

This research is partially supported by Naresuan university. The authors would like to thank the reviewers for their thoughtful comments and efforts towards improving our paper.

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Authors and Affiliations

  1. Department of Mathematics, Naresuan University, Phitsanulok, 65000, Thailand

    Anteneh Getachew Gebrie & Rabian Wangkeeree

  2. Research center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok, 65000, Thailand

    Rabian Wangkeeree

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  1. Anteneh Getachew Gebrie
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  2. Rabian Wangkeeree
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Correspondence to Rabian Wangkeeree.

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Gebrie, A.G., Wangkeeree, R. Parallel proximal method of solving split system of fixed point set constraint minimization problems. RACSAM 114, 13 (2020). https://doi.org/10.1007/s13398-019-00758-6

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