4.3 Article

NEW INERTIAL METHOD FOR GENERALIZED SPLIT VARIATIONAL INCLUSION PROBLEMS

Journal

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
Volume 17, Issue 6, Pages 3357-3371

Publisher

AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/jimo.2020123

Keywords

Maximal monotone operator; resolvent operator; inertial method; weak convergence; Hilbert space

Funding

  1. National Research Foundation (NRF) of South Africa [111992]
  2. Thailand Science Research and Innovation [IRN62W0007]
  3. Thailand Research Fund
  4. University of Phayao [RSA6180084]

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This paper introduces a new inertial iterative method for solving split variational inclusion problems in real Hilbert spaces. The method increases the rate of convergence by inertial extrapolation step, relaxes the choice of inertial factor, and shows numerical efficiency and superiority through test examples.
The purpose of this paper is to introduce a new inertial iterative method for solving split variational inclusion problems in real Hilbert spaces. We prove that the generated sequence converges weakly to the solution of the considered problem under some mild conditions. The major contributions of our results are: (i) to increase the rate of convergence of the method for solving split variational inclusion problem through the inertial extrapolation step, (ii) to relax the choice of the inertial factor and show the inertial factor can be chosen greater than 1/3 unlike what is previously known before for inertial proximal point method in the literature (iii) to show the numerical efficiency and superiority of our proposed method through some test example.

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