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Strong Convergence of Forward–Reflected–Backward Splitting Methods for Solving Monotone Inclusions with Applications to Image Restoration and Optimal Control by Chinedu Izuchukwu; Simeon Reich; Yekini Shehu; Adeolu Taiwo is a Engineering article available to read on EtoBox.

What is Strong Convergence of Forward–Reflected–Backward Splitting Methods for Solving Monotone Inclusions with Applications to Image Restoration and Optimal Control about?

In this paper, we propose and study several strongly convergent versions of the forwardreflected-backward splitting method of Malitsky and Tam for finding a zero of the sum of two monotone operators in a real Hilbert space. Our proposed methods only require one forward evaluation of the single-valued operator and one backward evaluation of the setvalued operator at each iteration; a feature that is absent in many other available strongly convergent splitting methods in the literature. We also develop inertial versions of our methods and strong convergence results are obtained for these methods when the set-valued operator is maximal monotone and the single-valued operator is Lipschitz continuous and monotone. Finally, we discuss some examples from image restorations and optimal control regarding the implementations of our methods in comparisons with known related methods in the literature.

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Author

Chinedu Izuchukwu; Simeon Reich; Yekini Shehu; Adeolu Taiwo

Publisher

Springer Science and Business Media LLC

Published

2023

Language

EN

Field

Engineering (Physical Sciences)