TY - JOUR
T1 - New hybrid three-term spectral-conjugate gradient method for finding solutions of nonlinear monotone operator equations with applications
AU - Abubakar, Auwal Bala
AU - Kumam, Poom
AU - Ibrahim, Abdulkarim Hassan
AU - Chaipunya, Parin
AU - Rano, Sadiya Ali
N1 - Publisher Copyright:
© 2021 International Association for Mathematics and Computers in Simulation (IMACS)
PY - 2022/11
Y1 - 2022/11
N2 - In this paper, we present a new hybrid spectral-conjugate gradient (SCG) algorithm for finding approximate solutions to nonlinear monotone operator equations. The hybrid conjugate gradient parameter has the Polak–Ribière–Polyak (PRP), Dai–Yuan (DY), Hestenes–Stiefel (HS) and Fletcher–Reeves (FR) as special cases. Moreover, the spectral parameter is selected such that the search direction has the descent property. Also, the search directions are bounded and the sequence of iterates generated by the new hybrid algorithm converge globally. Furthermore, numerical experiments were conducted on some benchmark nonlinear monotone operator equations to assess the efficiency of the proposed algorithm. Finally, the algorithm is shown to have the ability to recover disturbed signals.
AB - In this paper, we present a new hybrid spectral-conjugate gradient (SCG) algorithm for finding approximate solutions to nonlinear monotone operator equations. The hybrid conjugate gradient parameter has the Polak–Ribière–Polyak (PRP), Dai–Yuan (DY), Hestenes–Stiefel (HS) and Fletcher–Reeves (FR) as special cases. Moreover, the spectral parameter is selected such that the search direction has the descent property. Also, the search directions are bounded and the sequence of iterates generated by the new hybrid algorithm converge globally. Furthermore, numerical experiments were conducted on some benchmark nonlinear monotone operator equations to assess the efficiency of the proposed algorithm. Finally, the algorithm is shown to have the ability to recover disturbed signals.
KW - Conjugate gradient
KW - Non-linear equations
KW - Projection map
KW - Signal recovery
UR - http://www.scopus.com/inward/record.url?scp=85111049000&partnerID=8YFLogxK
U2 - 10.1016/j.matcom.2021.07.005
DO - 10.1016/j.matcom.2021.07.005
M3 - Article
AN - SCOPUS:85111049000
SN - 0378-4754
VL - 201
SP - 670
EP - 683
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
ER -