TY - JOUR
T1 - A MODIFIED LIU-STOREY-CONJUGATE DESCENT HYBRID PROJECTION METHOD FOR CONVEX CONSTRAINED NONLINEAR EQUATIONS AND IMAGE RESTORATION
AU - Ibrahim, Abdulkarim Hassan
AU - Deepho, Jitsupa
AU - Abubakar, Auwal Bala
AU - Aremu, Kazeem Olalekan
N1 - Publisher Copyright:
© 2022, American Institute of Mathematical Sciences. All rights reserved.
PY - 2022/9
Y1 - 2022/9
N2 - We present an iterative method for solving the convex constraint nonlinear equation problem. The method incorporates the projection strategy by Solodov and Svaiter with the hybrid Liu-Storey and Conjugate descent method by Yang et al. for solving the unconstrained optimization problem. The proposed method does not require the Jacobian information, nor does it require to store any matrix at each iteration. Thus, it has the potential to solve large-scale non-smooth problems. Under some standard assumptions, the convergence analysis of the method is established. Finally, to show the applicability of the proposed method, the proposed method is used to solve the ℓ1-norm regularized problems to restore blurred and noisy images. The numerical experiment indicates that our result is a significant improvement compared with the related methods for solving the convex constraint nonlinear equation problem.
AB - We present an iterative method for solving the convex constraint nonlinear equation problem. The method incorporates the projection strategy by Solodov and Svaiter with the hybrid Liu-Storey and Conjugate descent method by Yang et al. for solving the unconstrained optimization problem. The proposed method does not require the Jacobian information, nor does it require to store any matrix at each iteration. Thus, it has the potential to solve large-scale non-smooth problems. Under some standard assumptions, the convergence analysis of the method is established. Finally, to show the applicability of the proposed method, the proposed method is used to solve the ℓ1-norm regularized problems to restore blurred and noisy images. The numerical experiment indicates that our result is a significant improvement compared with the related methods for solving the convex constraint nonlinear equation problem.
KW - Conjugate gradient method
KW - Global convergence
KW - Nonlinear equations
KW - Projection method
UR - http://www.scopus.com/inward/record.url?scp=85133398869&partnerID=8YFLogxK
U2 - 10.3934/naco.2021022
DO - 10.3934/naco.2021022
M3 - Article
AN - SCOPUS:85133398869
SN - 2155-3289
VL - 12
SP - 569
EP - 582
JO - Numerical Algebra, Control and Optimization
JF - Numerical Algebra, Control and Optimization
IS - 3
ER -