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Relaxed inertial fixed point method for infinite family of averaged quasi-nonexpansive mapping with applications to sparse signal recovery

  • Optimization
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Abstract

It is known that several optimization problems can be converted to a fixed point problem for which the underline fixed point operator is an averaged quasi-nonexpansive mapping and thus the corresponding fixed point method utilizes to solve the considered optimization problem. In this paper, we consider a fixed point method involving inertial extrapolation step with relaxation parameter to obtain a common fixed point of a countable family of averaged quasi-nonexpansive mappings in real Hilbert spaces. Our results bring a unification of several versions of fixed point methods for averaged quasi-nonexpansive mappings considered in the literature and give several implications of our results. We also give some applications to monotone inclusion problem with three-operator splitting method and composite convex and non-convex relaxed inertial proximal methods to solve both convex and nonconvex reweighted \(l_Q\) regularization for recovering a sparse signal. Finally, some numerical experiments are drawn from sparse signal recovery to illustrate our theoretical results.

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Acknowledgements

This paper is dedicated to the loving memory of late Professor Charles Ejike Chidume (1947–2021).

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Correspondence to Yekini Shehu.

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Shehu, Y., Dong, QL., Hu, Z. et al. Relaxed inertial fixed point method for infinite family of averaged quasi-nonexpansive mapping with applications to sparse signal recovery. Soft Comput 26, 1793–1809 (2022). https://doi.org/10.1007/s00500-021-06416-7

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