Volume 33, Issue 4
Spectral DY-Type Projection Method for Nonlinear Monotone Systems of Equations

Jinkui Liu & Shengjie Li

J. Comp. Math., 33 (2015), pp. 341-355.

Published online: 2015-08

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  • Abstract

In this paper, we propose a spectral DY-type projection method for nonlinear monotone systems of equations, which is a reasonable combination of DY conjugate gradient method, the spectral gradient method and the projection technique. Without the differentiability assumption on the system of equations, we establish the global convergence of the proposed method, which does not rely on any merit function. Furthermore, this method is a derivative-free method and so is very suitable to solve large-scale nonlinear monotone systems of equations. The preliminary numerical results show the feasibility and effectiveness of the proposed method.

  • Keywords

Nonlinear monotone system of equations spectral gradient method DY conjugate gradient method Projection method Global convergence

  • AMS Subject Headings

65F10 65K05.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

liujinkui2006@126.com (Jinkui Liu)

lisj@cqu.edu.cn (Shengjie Li)

  • BibTex
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  • TXT
@Article{JCM-33-341, author = {Liu , Jinkui and Li , Shengjie }, title = {Spectral DY-Type Projection Method for Nonlinear Monotone Systems of Equations}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {4}, pages = {341--355}, abstract = {

In this paper, we propose a spectral DY-type projection method for nonlinear monotone systems of equations, which is a reasonable combination of DY conjugate gradient method, the spectral gradient method and the projection technique. Without the differentiability assumption on the system of equations, we establish the global convergence of the proposed method, which does not rely on any merit function. Furthermore, this method is a derivative-free method and so is very suitable to solve large-scale nonlinear monotone systems of equations. The preliminary numerical results show the feasibility and effectiveness of the proposed method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1412-m4494}, url = {http://global-sci.org/intro/article_detail/jcm/9847.html} }
TY - JOUR T1 - Spectral DY-Type Projection Method for Nonlinear Monotone Systems of Equations AU - Liu , Jinkui AU - Li , Shengjie JO - Journal of Computational Mathematics VL - 4 SP - 341 EP - 355 PY - 2015 DA - 2015/08 SN - 33 DO - http://doi.org/10.4208/jcm.1412-m4494 UR - https://global-sci.org/intro/article_detail/jcm/9847.html KW - Nonlinear monotone system of equations KW - spectral gradient method KW - DY conjugate gradient method KW - Projection method KW - Global convergence AB -

In this paper, we propose a spectral DY-type projection method for nonlinear monotone systems of equations, which is a reasonable combination of DY conjugate gradient method, the spectral gradient method and the projection technique. Without the differentiability assumption on the system of equations, we establish the global convergence of the proposed method, which does not rely on any merit function. Furthermore, this method is a derivative-free method and so is very suitable to solve large-scale nonlinear monotone systems of equations. The preliminary numerical results show the feasibility and effectiveness of the proposed method.

Jinkui Liu & Shengjie Li . (2020). Spectral DY-Type Projection Method for Nonlinear Monotone Systems of Equations. Journal of Computational Mathematics. 33 (4). 341-355. doi:10.4208/jcm.1412-m4494
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