Application of a new accelerated algorithm to regression problems

  • Avinash Dixit
  • D. R. Sahu
  • Amit Kumar SinghEmail author
  • T. Som
Methodologies and Application


Many iterative algorithms like Picard, Mann, Ishikawa are very useful to solve fixed point problems of nonlinear operators in real Hilbert spaces. The recent trend is to enhance their convergence rate abruptly by using inertial terms. The purpose of this paper is to investigate a new inertial iterative algorithm for finding the fixed points of nonexpansive operators in the framework of Hilbert spaces. We study the weak convergence of the proposed algorithm under mild assumptions. We apply our algorithm to design a new accelerated proximal gradient method. This new proximal gradient technique is applied to regression problems. Numerical experiments have been conducted for regression problems with several publicly available high-dimensional datasets and compare the proposed algorithm with already existing algorithms on the basis of their performance for accuracy and objective function values. Results show that the performance of our proposed algorithm overreaches the other algorithms, while keeping the iteration parameters unchanged.


Nonexpansive mapping S-iteration method Regression Composite minimization problems 



The first author would like to acknowledge the financial support by Indian Institute of Technology (Banaras Hindu University) in terms of teaching assistantship. The third author thankfully acknowledges the Council of Scientific and Industrial Research (CSIR), New Delhi, India, through University Grant Commission (UGC) for providing financial assistance in the form of Junior Research Fellowship through grant (Ref. No. 19/06/2016 (i) EU-V).

Compliance with ethical standards

Conflict of interest

There is no conflict of interest among all authors.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesIndian Institute of Technology (BHU)VaranasiIndia
  2. 2.Department of Mathematics, Institute of ScienceBanaras Hindu UniversityVaranasiIndia

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