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

Yanlai Song and Mihai Postolache
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Yanlai Song: College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China
Mihai Postolache: Department of General Education, China Medical University, Taichung 40402, Taiwan

Mathematics, 2021, vol. 9, issue 12, 1-17

Abstract: 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.

Keywords: hybrid steepest decent method; forward–backward method; quasi-variational inclusion problem; Banach space; variational inequality problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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