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Regularization of proximal point algorithms in Hadamard manifolds

  • Qamrul Hasan AnsariEmail author
  • Feeroz Babu
  • Jen-Chih Yao
Article
  • 45 Downloads

Abstract

In this paper, we consider the regularization method for exact as well as for inexact proximal point algorithms for finding the singularities of maximal monotone set-valued vector fields. We prove that the sequences generated by these algorithms converge to an element of the set of singularities of a maximal monotone set-valued vector field. A numerical example is provided to illustrate the inexact proximal point algorithm with regularization. Applications of our results to minimization problems and saddle point problems are given in the setting of Hadamard manifolds.

Keywords

Inclusion problems regularization method proximal point algorithms maximal monotone vector fields minimization problems saddle point problems Hadamard manifolds 

Mathematics Subject Classification

49J53 49J40 47H05 47J22 

Notes

Acknowledgements

The authors are grateful to the reviewers for their valuable suggestions and corrections that improved the first draft of this paper. In this research, the first author was supported by a research Grant of DST-SERB No. EMR/2016/005124, and the last author was supported by a research Grant No. MOST 105-2115-M-039-002-MY3.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia
  2. 2.Department of Mathematics and StatisticsKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia
  3. 3.Research Center for International Computing, China Medical University HospitalChina Medical UniversityTaichungTaiwan

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