Re-modified derivative-free iterative method for nonlinear monotone equations with convex constraints

Abstract In this note, we propose a modification as an alternative to remove the assumption of uniformly monotone as assumed in Aliyu et al. (2019). Numerical experiment shows that the modification improves the numerical performance of the method.

[1]  Weijun,et al.  LIMITED MEMORY BFGS METHOD FOR NONLINEAR MONOTONE EQUATIONS , 2007 .

[2]  Chuanwei Wang,et al.  A projection method for a system of nonlinear monotone equations with convex constraints , 2007, Math. Methods Oper. Res..

[3]  Poom Kumam,et al.  A Family of Derivative-Free Conjugate Gradient Methods for Constrained Nonlinear Equations and Image Restoration , 2020, IEEE Access.

[4]  Poom Kumam,et al.  A modified conjugate gradient method for monotone nonlinear equations with convex constraints , 2019, Applied Numerical Mathematics.

[5]  Poom Kumam,et al.  An efficient gradient-free projection algorithm for constrained nonlinear equations and image restoration , 2021 .

[6]  Jianhua Ma,et al.  Multivariate spectral gradient projection methodfor nonlinear monotone equations with convex constraints , 2012 .

[7]  Yunhai Xiao,et al.  A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing , 2013 .

[8]  Hassan Mohammad,et al.  A note on the spectral gradient projection method for nonlinear monotone equations with applications , 2020, Comput. Appl. Math..

[9]  J. Borwein,et al.  Two-Point Step Size Gradient Methods , 1988 .

[10]  Poom Kumam,et al.  A hybrid conjugate gradient algorithm for constrained monotone equations with application in compressive sensing , 2020, Heliyon.

[11]  Poom Kumam,et al.  Least-Square-Based Three-Term Conjugate Gradient Projection Method for ℓ1-Norm Problems with Application to Compressed Sensing , 2020, Mathematics.

[12]  José Mario Martínez,et al.  Spectral residual method without gradient information for solving large-scale nonlinear systems of equations , 2006, Math. Comput..

[13]  Yang Bing,et al.  AN EFFICIENT IMPLEMENTATION OF MERRILL'S METHOD FOR SPARSE OR PARTIALLY SEPARABLE SYSTEMS OF NONLINEAR EQUATIONS* , 1991 .

[14]  Shengjie Li,et al.  A projection method for convex constrained monotone nonlinear equations with applications , 2015, Comput. Math. Appl..

[15]  Keyvan Amini,et al.  A modified Hestenes–Stiefel conjugate gradient method with an optimal property , 2019, Optim. Methods Softw..

[16]  S. J. Li,et al.  A self-adaptive three-term conjugate gradient method for monotone nonlinear equations with convex constraints , 2016 .

[17]  William La Cruz A spectral algorithm for large-scale systems of nonlinear monotone equations , 2017, Numerical Algorithms.