Approximating solutions of split equality of some nonlinear optimization problems using an inertial algorithm

Lateef O. Jolaoso; Oluwatosin T. Mewomo

Commentationes Mathematicae Universitatis Carolinae (2020)

  • Volume: 61, Issue: 3, page 277-312
  • ISSN: 0010-2628

Abstract

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This paper presents an inertial iterative algorithm for approximating a common solution of split equalities of generalized mixed equilibrium problem, monotone variational inclusion problem, variational inequality problem and common fixed point problem in real Hilbert spaces. The algorithm is designed in such a way that it does not require prior knowledge of the norms of the bounded linear operators. We prove a strong convergence theorem under some mild conditions of the control sequences and also give a numerical example to show the efficiency and accuracy of our algorithm. We see that the inertial algorithm performs better in terms of number of iteration and CPU-time than the non-inertial algorithm. This result improves and generalizes many recent results in the literature.

How to cite

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Jolaoso, Lateef O., and Mewomo, Oluwatosin T.. "Approximating solutions of split equality of some nonlinear optimization problems using an inertial algorithm." Commentationes Mathematicae Universitatis Carolinae 61.3 (2020): 277-312. <http://eudml.org/doc/297146>.

@article{Jolaoso2020,
abstract = {This paper presents an inertial iterative algorithm for approximating a common solution of split equalities of generalized mixed equilibrium problem, monotone variational inclusion problem, variational inequality problem and common fixed point problem in real Hilbert spaces. The algorithm is designed in such a way that it does not require prior knowledge of the norms of the bounded linear operators. We prove a strong convergence theorem under some mild conditions of the control sequences and also give a numerical example to show the efficiency and accuracy of our algorithm. We see that the inertial algorithm performs better in terms of number of iteration and CPU-time than the non-inertial algorithm. This result improves and generalizes many recent results in the literature.},
author = {Jolaoso, Lateef O., Mewomo, Oluwatosin T.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {split equality; generalized equilibrium problem; variational inclusion problem; variational inequality; quasi-nonexpansive mapping; fixed point problem},
language = {eng},
number = {3},
pages = {277-312},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Approximating solutions of split equality of some nonlinear optimization problems using an inertial algorithm},
url = {http://eudml.org/doc/297146},
volume = {61},
year = {2020},
}

TY - JOUR
AU - Jolaoso, Lateef O.
AU - Mewomo, Oluwatosin T.
TI - Approximating solutions of split equality of some nonlinear optimization problems using an inertial algorithm
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 3
SP - 277
EP - 312
AB - This paper presents an inertial iterative algorithm for approximating a common solution of split equalities of generalized mixed equilibrium problem, monotone variational inclusion problem, variational inequality problem and common fixed point problem in real Hilbert spaces. The algorithm is designed in such a way that it does not require prior knowledge of the norms of the bounded linear operators. We prove a strong convergence theorem under some mild conditions of the control sequences and also give a numerical example to show the efficiency and accuracy of our algorithm. We see that the inertial algorithm performs better in terms of number of iteration and CPU-time than the non-inertial algorithm. This result improves and generalizes many recent results in the literature.
LA - eng
KW - split equality; generalized equilibrium problem; variational inclusion problem; variational inequality; quasi-nonexpansive mapping; fixed point problem
UR - http://eudml.org/doc/297146
ER -

References

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