TY - JOUR
T1 - A Derivative-Free Multivariate Spectral Projection Algorithm for Constrained NonLinear Monotone Equations
AU - Mohammad, Hassan
AU - Waziri, Mohammed Yusuf
AU - Abubakar, Auwal Bala
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.
PY - 2021/4
Y1 - 2021/4
N2 - In this paper, we present a derivative-free multivariate spectral projection algorithm for convex constrained nonlinear monotone equations. The search direction is a product of a convex combination of two different spectral diagonal matrices and the residual vector. Moreover, to ensure positive definiteness of the diagonal matrix associated with the search direction, suitable safeguard is formulated. Some of the remarkable properties of the algorithm include: Jacobian free approach, capacity to solve large-scale problems and the search direction generated by the algorithm, satisfy the descent property independent on the line search employed. Under appropriate assumptions, the global convergence of the algorithm is given. Numerical experiments show that the algorithm has advantages over the recently proposed multivariate derivative-free projection algorithm by Liu and Li (J Ind Manag Optim 13(1):283–295, 2017) and also compete with another algorithm having the standard choice of the Barzilai-Borwein step as the search direction.
AB - In this paper, we present a derivative-free multivariate spectral projection algorithm for convex constrained nonlinear monotone equations. The search direction is a product of a convex combination of two different spectral diagonal matrices and the residual vector. Moreover, to ensure positive definiteness of the diagonal matrix associated with the search direction, suitable safeguard is formulated. Some of the remarkable properties of the algorithm include: Jacobian free approach, capacity to solve large-scale problems and the search direction generated by the algorithm, satisfy the descent property independent on the line search employed. Under appropriate assumptions, the global convergence of the algorithm is given. Numerical experiments show that the algorithm has advantages over the recently proposed multivariate derivative-free projection algorithm by Liu and Li (J Ind Manag Optim 13(1):283–295, 2017) and also compete with another algorithm having the standard choice of the Barzilai-Borwein step as the search direction.
KW - Derivative-free method
KW - Global convergence
KW - Multivariate spectral method
KW - Nonlinear monotone equations
KW - Projection method
UR - http://www.scopus.com/inward/record.url?scp=85103371205&partnerID=8YFLogxK
U2 - 10.1007/s40819-021-00995-7
DO - 10.1007/s40819-021-00995-7
M3 - Article
AN - SCOPUS:85103371205
SN - 2349-5103
VL - 7
JO - International Journal of Applied and Computational Mathematics
JF - International Journal of Applied and Computational Mathematics
IS - 2
M1 - 55
ER -