×

zbMATH — the first resource for mathematics

A family of conjugate gradient methods for large-scale nonlinear equations. (English) Zbl 1371.90101
Summary: In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved. Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying mapping. Preliminary numerical results are reported to show the efficiency of the proposed method.

MSC:
90C25 Convex programming
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
Software:
MCPLIB
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Wang, YJ, Caccetta, L, Zhou, GL: Convergence analysis of a block improvement method for polynomial optimization over unit spheres. Numer. Linear Algebra Appl. 22, 1059-1076 (2015) · Zbl 1374.65105
[2] Zeidler, E: Nonlinear Functional Analysis and Its Applications. Springer, Berlin (1990) · Zbl 0684.47029
[3] Wang, CW, Wang, YJ: A superlinearly convergent projection method for constrained systems of nonlinear equations. J. Glob. Optim. 40, 283-296 (2009) · Zbl 1191.90072
[4] Wang, YJ, Caccetta, L, Zhou, GL: Convergence analysis of a block improvement method for polynomial optimization over unit spheres. Numer. Linear Algebra Appl. 22, 1059-1076 (2015) · Zbl 1374.65105
[5] Wood, AJ, Wollenberg, BF: Power Generation, Operation, and Control. Wiley, New York (1996)
[6] Chen, HB, Wang, YJ, Zhao, HG: Finite convergence of a projected proximal point algorithm for the generalized variational inequalities. Oper. Res. Lett. 40, 303-305 (2012) · Zbl 1247.90264
[7] Dirkse, SP, Ferris, MC: MCPLIB: A collection of nonlinear mixed complementarity problems. Optim. Methods Softw. 5, 319-345 (1995)
[8] Wang, YJ, Qi, L, Luo, S, Xu, Y: An alternative steepest direction method for the optimization in evaluating geometric discord. Pac. J. Optim. 10, 137-149 (2014) · Zbl 1285.81008
[9] Zhang, L, Zhou, W: Spectral gradient projection method for solving nonlinear monotone equations. J. Comput. Appl. Math. 196, 478-484 (2006) · Zbl 1128.65034
[10] Yu, ZS, Lin, J, Sun, J, Xiao, YH, Liu, LY, Li, ZH: Spectral gradient projection method for monotone nonlinear equations with convex constraints. Appl. Numer. Math. 59, 2416-2423 (2009) · Zbl 1183.65056
[11] Ma, FM, Wang, CW: Modified projection method for solving a system of monotone equations with convex constraints. J. Appl. Math. Comput. 34, 47-56 (2010) · Zbl 1225.90128
[12] Zheng, L: A new projection algorithm for solving a system of nonlinear equations with convex constraints. Bull. Korean Math. Soc. 50, 823-832 (2013) · Zbl 1273.90158
[13] Sun, M, Wang, YJ, Liu, J: Generalized Peaceman-Rachford splitting method for multiple-block separable convex programming with applications to robust PCA. Calcolo 54, 77-94 (2017) · Zbl 1368.90129
[14] Li, M, Qu, AP: Some sufficient descent conjugate gradient methods and their global convergence. Comput. Appl. Math. 33, 333-347 (2014) · Zbl 1307.90171
[15] Karamardian, S: Complementarity problems over cones with monotone and pseudomonotone maps. J. Optim. Theory Appl. 18, 445-454 (1976) · Zbl 0304.49026
[16] Xiao, YH, 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) · Zbl 1316.90050
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.