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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]
Copyright of Journal of Computational & Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 192840383
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Two inertial multistep projection-type algorithms for solving mixed split feasibility problems in Hilbert space.
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  Data: <searchLink fieldCode="AR" term="%22Ha%2C+Nguyen+Song%22">Ha, Nguyen Song</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hans@tnus.edu.vn</i><br /><searchLink fieldCode="AR" term="%22Reich%2C+Simeon%22">Reich, Simeon</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> sreich@technion.ac.il</i><br /><searchLink fieldCode="AR" term="%22Tuyen%2C+Truong+Minh%22">Tuyen, Truong Minh</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> tuyentm@tnus.edu.vn</i><br /><searchLink fieldCode="AR" term="%22Thu%2C+Pham+Thi%22">Thu, Pham Thi</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> phamthithu@tnut.edu.vn</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+%26+Applied+Mathematics%22">Journal of Computational & Applied Mathematics</searchLink>. Oct2026, Vol. 484, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink><br /><searchLink fieldCode="DE" term="%22Feasibility+problem+%28Mathematical+optimization%29%22">Feasibility problem (Mathematical optimization)</searchLink><br /><searchLink fieldCode="DE" term="%22Relaxation+methods+%28Mathematics%29%22">Relaxation methods (Mathematics)</searchLink>
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  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Journal of Computational & Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.cam.2026.117507
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      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Hilbert space
        Type: general
      – SubjectFull: Feasibility problem (Mathematical optimization)
        Type: general
      – SubjectFull: Relaxation methods (Mathematics)
        Type: general
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      – TitleFull: Two inertial multistep projection-type algorithms for solving mixed split feasibility problems in Hilbert space.
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            NameFull: Ha, Nguyen Song
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            NameFull: Reich, Simeon
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            NameFull: Tuyen, Truong Minh
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            NameFull: Thu, Pham Thi
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            – D: 01
              M: 10
              Text: Oct2026
              Type: published
              Y: 2026
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