Forward-backward splitting algorithm with self-adaptive method for finite family of split minimization and fixed point problems in Hilbert spaces

Hammed Anuoluwapo Abbas; Kazeem Aremu; Olawale Oyewole; Akindele Mebawondu; Ojen Narain

doi:10.33993/jnaat522-1351

Authors

Hammed Anuoluwapo Abbas Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Science University, Ga-Rankuwa, South Africa https://orcid.org/0000-0002-4236-3278
Kazeem Aremu Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Science University, Ga-Rankuwa, South Africa
Olawale Oyewole School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
Akindele Mebawondu Department of Computer Science and Mathematics, Mountain Top University, Prayer City, Nigeria
Ojen Narain School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

DOI:

https://doi.org/10.33993/jnaat522-1351

Keywords:

Nonexpansive mapping, minimization problem, inertial method, forward-backward splitting method, fixed point problem

Abstract views: 105

Abstract

In this paper, we introduce an inertial forward-backward splitting method together with a Halpern iterative algorithm for approximating a common solution of a finite family of split minimization problem involving two proper, lower semicontinuous and convex functions and fixed point problem of a nonexpansive mapping in real Hilbert spaces. Under suitable conditions, we proved that the sequence generated by our algorithm converges strongly to a solution of the aforementioned problems. The stepsizes studied in this paper are designed in such a way that they do not require the Lipschitz continuity condition on the gradient and prior knowledge of operator norm. Finally, we illustrate a numerical experiment to show the performance of the proposed method. The result discussed in this paper extends and complements many related results in literature.

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References

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