More Web Proxy on the site http://driver.im/

article

New hybrid conjugate gradient projection method for the convex constrained equations

Authors:

Jing LiuAuthors Info & Claims

Calcolo, Volume 53, Issue 3

Pages 399 - 411

https://doi.org/10.1007/s10092-015-0154-z

Published: 01 September 2016 Publication History

Abstract

Based on the two famous Hestenes---Stiefel and Dai---Yuan conjugate gradient methods, a new hybrid conjugate gradient projection method is proposed for the convex constrained equations. At each iteration, the new method is fully free from any derivative evaluations. Furthermore, the search direction generated by the proposed method satisfies the sufficient descent property, which is independent of the line search. Under the condition that the underlying mapping is continuous and monotone, we establish the global convergence of the new method. Compared with traditional methods for solving such problem, our new method does not require the Lipschitz continuity of the underlying mapping. Some large-scale numerical tests are performed and reported, which show that the proposed method is efficient and promising.

References

[1]

Meintjes, K., Morgan, A.P.: A methodology for solving chemical equilibrium systems. Appl. Math. Comput. 22, 333---361 (1987)

Digital Library

[2]

Dirkse, S.P., Ferris, M.C.: MCPLIB: a collection of nonlinear mixed complementarity problems. Optim. Methods Softw. 5, 319---345 (1995)

[3]

Xiao, Y.H., Zhu, H.: A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing. J. Math. Anal. Appl. 405, 310---319 (2013)

[4]

Han, D.R.: A proximal decomposition algorithm for variational inequality problems. J. Comput. Appl. Math. 161(1), 231---244 (2003)

Digital Library

[5]

Wang, C.W., Wang, Y.J., Xu, C.L.: A projection method for a system of nonlinear monotone equations with convex constraints. Math. Methods Oper. Res. 66, 33---46 (2007)

[6]

Zhang, L., Zhou, W.J.: Spectral gradient projection method for solving nonlinear monotone equations. J. Comput. Appl. Math. 196(2), 478---484 (2006)

Digital Library

[7]

Cheng, W.Y.: A PRP type method for systems of monotone equations. Math. Comput. Model. 50(1---2), 15---20 (2009)

Digital Library

[8]

Yu, Z.S., Lin, J., Sun, J., Xiao, Y.H., Liu, L.Y., Li, Z.H.: Spectral gradient projection method for monotone nonlinear equations with convex constraints. Appl. Numer. Math. 59, 2416---2423 (2009)

Digital Library

[9]

Liu, S.Y., Huang, Y.Y, Jiao, H.W.: Sufficient descent conjugate gradient methods for solving convex constrained nonlinear monotone equations. Abstr. Appl. Anal. 2014, 12 (2014)

[10]

Sun, M., Liu, J.: Three derivative-free projection methods for large-scale nonlinear equations with convex constraints. J. Appl. Math. Comput. 47(1---2), 265---276 (2015)

[11]

Fletcher, R., Reeves, C.: Function minimization by conjugate gradients. J. Comput. 7, 149---154 (1964)

[12]

Polak, B., Ribière, G.: Note surla convergence des méthodes de directions conjuguées. Rev. Francaise Imformat Rech. Opertionelle 16, 35---43 (1969)

[13]

Gilber, J.C., Nocedal, J.: Global convergence properties of conjugate gradient methods for optimization. SIAM J. Optim. 2, 21---42 (1992)

[14]

Hestenes, M.R., Stiefel, E.L.: Method of conjugate gradient for solving linear systems. J. Res. Natl. Bur. Stand. 49, 409---432 (1952)

[15]

Dai, Y.H., Yuan, Y.X.: A nonlinear conjugate gradient method with a strong global convergence property. SIAM J. Optim. 10, 177---182 (2000)

Digital Library

[16]

Jian, J.B., Han, L., Jiang, X.Z.: A hybrid conjugate gradient method with descent property for unconstrained optimization. Appl. Math. Model. 39(3---4), 1281---1290 (2015)

[17]

Hu, Y.P., Wei, Z.X.: Wei---Yao---Liu conjugate gradient projection algorithm for nonlinear monotone equations with convex constraints. Int. J. Comput. Math. (2014).

Digital Library

[18]

Wang, X.Y., Li, S.J., Kou, X.P.: A self-adaptive three-term conjugate gradient method for monotone nonlinear equations with convex constraints. Calcolo (2015).

Digital Library

[19]

Wei, Z.X., Yao, S.W., Liu, L.Y.: The convergence properties of some new conjugate gradient methods. Appl. Math. Comput. 183, 1341---1350 (2006)

[20]

Yao, S.W., Wei, Z.X., Huang, H.: A note about WYL's conjugate gradient method and its application. Appl. Math. Comput. 191, 381---388 (2007)

Digital Library

Cited By

Jiang XHuang Z(2024)An accelerated relaxed-inertial strategy based CGP algorithm with restart technique for constrained nonlinear pseudo-monotone equations to image de-blurring problemsJournal of Computational and Applied Mathematics10.1016/j.cam.2024.115887447:COnline publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1016/j.cam.2024.115887
Abubakar AIbrahim AAbdullahi MAphane MChen J(2024)A sufficient descent LS-PRP-BFGS-like method for solving nonlinear monotone equations with application to image restorationNumerical Algorithms10.1007/s11075-023-01673-z96:4(1423-1464)Online publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1007/s11075-023-01673-z
Yin JJian JJiang XLiu MWang L(2021)A hybrid three-term conjugate gradient projection method for constrained nonlinear monotone equations with applicationsNumerical Algorithms10.1007/s11075-020-01043-z88:1(389-418)Online publication date: 1-Sep-2021
https://dl.acm.org/doi/10.1007/s11075-020-01043-z

New hybrid conjugate gradient projection method for the convex constrained equations

Recommendations

A modified Polak-Ribière-Polyak conjugate gradient algorithm for nonsmooth convex programs

The conjugate gradient (CG) method is one of the most popular methods for solving smooth unconstrained optimization problems due to its simplicity and low memory requirement. However, the usage of CG methods is mainly restricted to solving smooth ...
A Barzilai and Borwein scaling conjugate gradient method for unconstrained optimization problems

In this paper, we combine the conjugate gradient method with the Barzilai and Borwein gradient method, and propose a Barzilai and Borwein scaling conjugate gradient method for nonlinear unconstrained optimization problems. The new method does not ...
A new subspace minimization conjugate gradient method with nonmonotone line search for unconstrained optimization

A new subspace minimization conjugate gradient algorithm with a nonmonotone Wolfe line search is proposed and analyzed. In the scheme, we propose two choices of the search direction by minimizing a quadratic approximation of the objective function in ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Calcolo: a quarterly on numerical analysis and theory of computation

Calcolo: a quarterly on numerical analysis and theory of computation Volume 53, Issue 3

September 2016

251 pages

ISSN:0008-0624

Issue’s Table of Contents

Copyright © Copyright © 2016 Springer-Verlag Italia.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 September 2016

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

3
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 16 Dec 2024

Other Metrics

View Author Metrics

Citations

Cited By

Jiang XHuang Z(2024)An accelerated relaxed-inertial strategy based CGP algorithm with restart technique for constrained nonlinear pseudo-monotone equations to image de-blurring problemsJournal of Computational and Applied Mathematics10.1016/j.cam.2024.115887447:COnline publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1016/j.cam.2024.115887
Abubakar AIbrahim AAbdullahi MAphane MChen J(2024)A sufficient descent LS-PRP-BFGS-like method for solving nonlinear monotone equations with application to image restorationNumerical Algorithms10.1007/s11075-023-01673-z96:4(1423-1464)Online publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1007/s11075-023-01673-z
Yin JJian JJiang XLiu MWang L(2021)A hybrid three-term conjugate gradient projection method for constrained nonlinear monotone equations with applicationsNumerical Algorithms10.1007/s11075-020-01043-z88:1(389-418)Online publication date: 1-Sep-2021
https://dl.acm.org/doi/10.1007/s11075-020-01043-z
Liu PJian JJiang X(2020)A New Conjugate Gradient Projection Method for Convex Constrained Nonlinear EquationsComplexity10.1155/2020/83238652020Online publication date: 1-Jan-2020
https://dl.acm.org/doi/10.1155/2020/8323865

View Options

View options

Media

Figures

Other

Tables

View Issue’s Table of Contents