A Derivative-Free Multivariate Spectral Projection Algorithm for Constrained NonLinear Monotone Equations

被引：0
作者：
Mohammad H. [1 ,2 ]
Waziri M.Y. [1 ,2 ]
Abubakar A.B. [1 ,3 ]
机构：
[1] Department of Mathematical Sciences, Faculty of Physical Science, Bayero University Kano, Kano, 700241, Kano
[2] Numerical Optimization Research Group, Bayero University, Kano
[3] Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria, Medunsa
来源：
International Journal of Applied and Computational Mathematics | 2021年 / 7卷 / 2期
关键词：
Derivative-free method; Global convergence; Multivariate spectral method; Nonlinear monotone equations; Projection method;
D O I：
10.1007/s40819-021-00995-7
中图分类号：
学科分类号：
摘要：
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. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.
引用
收藏
相关论文
共 45 条
[1]  
Abubakar A.B., Kumam P., An improved three-term derivative-free method for solving nonlinear equations, Comput. Appl. Math., 37, pp. 6760-6773, (2018)
[2]  
Abubakar A.B., Kumam P., Mohammad H., A note on the spectral gradient projection method for nonlinear monotone equations with applications, Comput. Appl. Math., 39, (2020)
[3]  
Ahookhosh M., Amini K., Bahrami S., Two derivative-free projection approaches for systems of large-scale nonlinear monotone equations, Numer. Algorithms, 64, 1, pp. 21-42, (2013)
[4]  
Awwal A.M., Kumam P., Mohammad H., Watthayu W., Abubakar A.B., A perry-type derivative-free algorithm for solving nonlinear system of equations and minimizing e l l 1 regularized problem, Optimization, (2020)
[5]  
Awwal A.M., Wang L., Kumam P., Mohammad H., A two-step spectral gradient projection method for system of nonlinear monotone equations and image deblurring problems, Symmetry, 12, 6, (2020)
[6]  
Barzilai J., Borwein J.M., Two-point step size gradient methods, IMA J. Numer. Anal., 8, 1, pp. 141-148, (1988)
[7]  
Bellavia S., Bertaccini D., Morini B., Nonsymmetric preconditioner updates in Newton-Krylov methods for nonlinear systems, SIAM J. Sci. Comput., 33, 5, pp. 2595-2619, (2011)
[8]  
Bing Y., Lin G., An efficient implementation of merrill’s method for sparse or partially separable systems of nonlinear equations, SIAM J. Optim., 1, 2, pp. 206-221, (1991)
[9]  
Dai Y.H., Al-Baali M., Yang X., A positive Barzilai-Borwein-like stepsize and an extension for symmetric linear systems, Numerical Analysis and Optimization, pp. 59-75, (2015)
[10]  
Dai Z., Chen X., Wen F., A modified perry’s conjugate gradient method-based derivative-free method for solving large-scale nonlinear monotone equations, Appl. Math. Comput., 270, pp. 378-386, (2015)
12345