TY - JOUR
T1 - Self-adaptive Forward–Backward Contraction-type Methods for Generalized Split Feasibility Problems
AU - Izuchukwu, Chinedu
AU - Jolaoso, Lateef Olakunle
AU - Nnakwe, Monday Ogudu
AU - Ugwunnadi, Godwin Chidi
AU - Khan, Abdul Rahim
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2022/10
Y1 - 2022/10
N2 - Based on the recent important results of Takahashi–Xu–Yao [Set-Valued and Variational Analysis 23(2015), 205–221] and other related results on split feasibility problems, we study a certain class of generalized split feasibility problems which includes many other split-type problems. We propose some new self-adaptive forward–backward contraction-type methods and prove that they converge strongly to a minimum-norm solution of the generalized split feasibility problems in real Hilbert spaces. As a by-product, we obtain self-adaptive methods for solving other classes of generalized split feasibility problems in real Hilbert spaces. Finally, we apply our results to solve an optimal control problem and an image restoration problem through numerical implementations, and compare our methods with related strongly convergent methods in the literature.
AB - Based on the recent important results of Takahashi–Xu–Yao [Set-Valued and Variational Analysis 23(2015), 205–221] and other related results on split feasibility problems, we study a certain class of generalized split feasibility problems which includes many other split-type problems. We propose some new self-adaptive forward–backward contraction-type methods and prove that they converge strongly to a minimum-norm solution of the generalized split feasibility problems in real Hilbert spaces. As a by-product, we obtain self-adaptive methods for solving other classes of generalized split feasibility problems in real Hilbert spaces. Finally, we apply our results to solve an optimal control problem and an image restoration problem through numerical implementations, and compare our methods with related strongly convergent methods in the literature.
KW - Generalized split feasibility problems
KW - contraction-type methods
KW - forward–backward algorithms
KW - optimal control sequences
KW - self-adaptive methods
UR - http://www.scopus.com/inward/record.url?scp=85137198813&partnerID=8YFLogxK
U2 - 10.1007/s00009-022-02114-2
DO - 10.1007/s00009-022-02114-2
M3 - Article
AN - SCOPUS:85137198813
SN - 1660-5446
VL - 19
JO - Mediterranean Journal of Mathematics
JF - Mediterranean Journal of Mathematics
IS - 5
M1 - 204
ER -