Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application

In this paper, we present a new modified inertial forward–backward algorithm for finding a common solution of the quasi-variational inclusion problem and the variational inequality problem in a q-uniformly smooth Banach space. The proposed algorithm is based on descent, splitting and inertial ideas....

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 9; no. 12; p. 1365
Main Authors: Song, Yanlai, Postolache, Mihai
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.06.2021
Subjects:
Algorithms
Banach space
Banach spaces
forward–backward method
Hilbert space
hybrid steepest decent method
Iterative algorithms
Iterative methods
Mathematics
quasi-variational inclusion problem
variational inequality problem
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary:In this paper, we present a new modified inertial forward–backward algorithm for finding a common solution of the quasi-variational inclusion problem and the variational inequality problem in a q-uniformly smooth Banach space. The proposed algorithm is based on descent, splitting and inertial ideas. Under suitable assumptions, we prove that the sequence generated by the iterative algorithm converges strongly to the unique solution of the abovementioned problems. Numerical examples are also given to demonstrate our results.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math9121365