TY - JOUR
T1 - Derivative-free SMR conjugate gradient method for constraint nonlinear equations
AU - Ibrahim, Abdulkarim Hassan
AU - Muangchoo, Kanikar
AU - Mohamed, Nur Syarafina
AU - Abubakard, Auwal Bala
N1 - Publisher Copyright:
© 2022, International Scientific Research Publications. All rights reserved.
PY - 2022
Y1 - 2022
N2 - Based on the SMR conjugate gradient method for unconstrained optimization proposed by Mohamed et al. [N. S. Mohamed, M. Mamat, M. Rivaie, S. M. Shaharuddin, Indones. J. Electr. Eng. Comput. Sci., 11 (2018), 1188-1193] and the Solodov and Svaiter projection technique, we propose a derivative-free SMR method for solving nonlinear equations with convex constraints. The proposed method can be viewed as an extension of the SMR method for solving unconstrained optimization. The proposed method can be used to solve large-scale nonlinear equations with convex constraints because of derivative-free and low storage. Under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity assumption, we prove its global convergence. Preliminary numerical results show that the proposed method is promising.
AB - Based on the SMR conjugate gradient method for unconstrained optimization proposed by Mohamed et al. [N. S. Mohamed, M. Mamat, M. Rivaie, S. M. Shaharuddin, Indones. J. Electr. Eng. Comput. Sci., 11 (2018), 1188-1193] and the Solodov and Svaiter projection technique, we propose a derivative-free SMR method for solving nonlinear equations with convex constraints. The proposed method can be viewed as an extension of the SMR method for solving unconstrained optimization. The proposed method can be used to solve large-scale nonlinear equations with convex constraints because of derivative-free and low storage. Under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity assumption, we prove its global convergence. Preliminary numerical results show that the proposed method is promising.
KW - Conjugate gradient method
KW - Global convergence
KW - Nonlinear equations
KW - Projection method
UR - http://www.scopus.com/inward/record.url?scp=85101499932&partnerID=8YFLogxK
U2 - 10.22436/JMCS.024.02.06
DO - 10.22436/JMCS.024.02.06
M3 - Article
AN - SCOPUS:85101499932
SN - 2008-949X
VL - 24
SP - 147
EP - 164
JO - Journal of Mathematics and Computer Science
JF - Journal of Mathematics and Computer Science
IS - 2
ER -