A generalized scheme for split inclusion problem with conjugate like direction

Jamilu Abubakar, Parin Chaipunya (), Poom Kumam and Sani Salisu
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Jamilu Abubakar: King Mongkut’s University of Technology Thonburi
Parin Chaipunya: King Mongkut’s University of Technology Thonburi
Poom Kumam: King Mongkut’s University of Technology Thonburi
Sani Salisu: King Mongkut’s University of Technology Thonburi

Mathematical Methods of Operations Research, 2025, vol. 101, issue 1, No 3, 71 pages

Abstract: Abstract This paper, we propose enhanced methods for solving the generalized split inclusion problem involving several maximally monotone operators. The proposed algorithms incorporate conjugate gradient methods technique, in particular, the conjugate direction approach into the CQ algorithm. We showed that the sequences generated by the proposed methods converges strongly under mild conditons. Additionally, we present numerical illustrations to demonstrate the convergence of the sequence generated by the proposed methods, validate our theoretical findings and showcase the computational performance of the proposed method.

Keywords: Inclusion problem; Split feasibility; Conjugate gradient method; Maximal monotone operator; CQ algorithm; Self-adaptive; 47H05; 47J20; 47J25; 65K15. (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00186-024-00882-z

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