TY - JOUR

T1 - Generalized Split Feasibility Problem

T2 - Solution by Iteration

AU - Enyi, Cyril Dennis

AU - Ezeora, Jeremiah Nkwegu

AU - Ugwunnadi, Godwin Chidi

AU - Nwawuru, Francis

AU - Mukiawa, Soh Edwin

N1 - Publisher Copyright:
© 2024, SINUS Association. All rights reserved.

PY - 2024

Y1 - 2024

N2 - In real Hilbert spaces, given a single-valued Lipschitz continuous and monotone operator, we study generalized split feasibility problem (GSFP) over solution set of monotone variational inclusion problem. An inertia iterative method is proposed to solve this problem, by showing that the sequence generated by the iteration converges strongly to solution of GSFP. As against previous methods, our step size is chosen to be simple and not depending on norm of associated bounded linear map as well as Lipschitz constant of the single-valued operator. The obtained result was applied to study split linear inverse problem, precisely, the LASSO problem. Lastly, with the aid of numerical examples, we exhibited efficiency of our algorithm and its dominance over other existing schemes.

AB - In real Hilbert spaces, given a single-valued Lipschitz continuous and monotone operator, we study generalized split feasibility problem (GSFP) over solution set of monotone variational inclusion problem. An inertia iterative method is proposed to solve this problem, by showing that the sequence generated by the iteration converges strongly to solution of GSFP. As against previous methods, our step size is chosen to be simple and not depending on norm of associated bounded linear map as well as Lipschitz constant of the single-valued operator. The obtained result was applied to study split linear inverse problem, precisely, the LASSO problem. Lastly, with the aid of numerical examples, we exhibited efficiency of our algorithm and its dominance over other existing schemes.

KW - Generalized split feasibility problem

KW - Hilbert space

KW - maximal monotone operator

KW - monotone variational inclusion problem

KW - resolvent operator

UR - http://www.scopus.com/inward/record.url?scp=85194224956&partnerID=8YFLogxK

U2 - 10.37193/CJM.2024.03.08

DO - 10.37193/CJM.2024.03.08

M3 - Article

AN - SCOPUS:85194224956

SN - 1584-2851

VL - 40

SP - 655

EP - 679

JO - Carpathian Journal of Mathematics

JF - Carpathian Journal of Mathematics

IS - 3

ER -