Geodesic
Inertial forward-backward splitting method in Banach spaces with application to compressed sensing
Applications of Mathematics, Tome 64 (2019) no. 4, pp. 409-435.

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We propose a Halpern-type forward-backward splitting with inertial extrapolation step for finding a zero of the sum of accretive operators in Banach spaces. Strong convergence of the sequence of iterates generated by the method proposed is obtained under mild assumptions. We give some numerical results in compressed sensing to validate the theoretical analysis results. Our result is one of the few available inertial-type methods for zeros of the sum of accretive operators in Banach spaces.
DOI : 10.21136/AM.2019.0323-18
Classification : 47H05, 47J20, 47J25
Keywords: inertial term; forward-backward splitting; inclusion problem; strong convergence; Banach space 
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     title = {Inertial forward-backward splitting method in {Banach} spaces with application to compressed sensing},
     journal = {Applications of Mathematics},
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Cholamjiak, Prasit; Shehu, Yekini. Inertial forward-backward splitting method in Banach spaces with application to compressed sensing. Applications of Mathematics, Tome 64 (2019) no. 4, pp. 409-435. doi : 10.21136/AM.2019.0323-18. http://geodesic.mathdoc.fr/articles/10.21136/AM.2019.0323-18/

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