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Two inertial multistep projection-type algorithms for solving mixed split feasibility problems in Hilbert space.

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Title: Two inertial multistep projection-type algorithms for solving mixed split feasibility problems in Hilbert space.
Authors: Ha, Nguyen Song1 (AUTHOR) hans@tnus.edu.vn, Reich, Simeon2 (AUTHOR) sreich@technion.ac.il, Tuyen, Truong Minh1 (AUTHOR) tuyentm@tnus.edu.vn, Thu, Pham Thi3 (AUTHOR) phamthithu@tnut.edu.vn
Source: Journal of Computational & Applied Mathematics. Oct2026, Vol. 484, pN.PAG-N.PAG. 1p.
Subjects: Hilbert space, Feasibility problem (Mathematical optimization), Relaxation methods (Mathematics)
Abstract: We study the mixed split feasibility problem in real Hilbert space. In order to find a solution to this problem, we use hybrid and shrinking projection methods to propose two new inertial multistep projection-type algorithms. A distinctive feature of our methods is that the inertial parameters are only required to be bounded, rather than diminishing or constrained to lie within fixed intervals such as [ − 1 , 1 ] or [0, a ], as is commonly imposed in many existing inertial schemes. This relaxation makes the selection of inertial factors more flexible and easier to implement while still ensuring strong convergence. In addition, the other control parameters are selected so that the implementation of our algorithm does not depend on any prior information regarding the norms of the transfer operators. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:We study the mixed split feasibility problem in real Hilbert space. In order to find a solution to this problem, we use hybrid and shrinking projection methods to propose two new inertial multistep projection-type algorithms. A distinctive feature of our methods is that the inertial parameters are only required to be bounded, rather than diminishing or constrained to lie within fixed intervals such as [ − 1 , 1 ] or [0, a ], as is commonly imposed in many existing inertial schemes. This relaxation makes the selection of inertial factors more flexible and easier to implement while still ensuring strong convergence. In addition, the other control parameters are selected so that the implementation of our algorithm does not depend on any prior information regarding the norms of the transfer operators. [ABSTRACT FROM AUTHOR]
ISSN:03770427
DOI:10.1016/j.cam.2026.117507