A derivative-free conjugate gradient projection method based on the memoryless BFGS update
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https://doi.org/10.26637/MJM0802/0031Abstract
Conjugate gradient-based projection methods are widely used for solving large-scale nonlinear monotone equations. This is due to their simplicity and that they are derivative-free. In this paper, we propose another conjugate gradient-based projection method for large-scale nonlinear monotone equations. We show that the method satisfies the descent condition independent of line searches and that the method is globally convergent. Numerical results show that the method is both efficient and effective
Keywords:
Global convergence, Nonlinear monotone equations, Derivative-freeMathematics Subject Classification:
Mathematics- Pages: 502-509
- Date Published: 01-04-2020
- Vol. 8 No. 02 (2020): Malaya Journal of Matematik (MJM)
A. B. Abubakar, P. Kumam, H. Mohammad and A. M. Awwal, An efficient conjugate gradient method for convex constrained monotone nonlinear equations with applications, Mathematics, 7:767 (2019), https://doi.org/10.3390/math7090767.
Y. Ding, Y. Xiao and J. Li, A class of conjugate gradient methods for convex constrained monotone equations, Optim., 66(12) (2017), 2309-2328.
E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles, Math. Program., 91 (2002), 201-213.
P. Gao and C. He, An effecient three-term conjugate gradient method for nonlinear monotone equations with convex constraints, Calcolo, 55:53 (2018), https://dx.doi.org/10.1007/s10092-018-0291-2.
P. Gao, C. He and Y. Liu, An adaptive family of projection methods for constrained monotone equations with applications, Appl. Math. Comput., 359 (2019), 1-16.
J. Guo and Z. Wan, A modified spectral PRP conjugate gradient projection method for solving large-scale monotone equations and its application in compressed sensing, Math. Prob. Eng., 2019 Article ID 5261830 (2019), 17 pages.
A.N. Iusem and M.V. Solodov, Newton-type methods with generalized distances for constrained optimization, Optim., 41 (1997), 257-278.
M. Koorapetse, P. Kaelo and E.R. Offen, A scaled derivative free projection method for solving nonlinear monotone equations, Bull. Iran. Math. Soc., 45 (2019), 755770.
J. Liu and S. Li, Multivariate spectral DY-type projection method for convex constrained nonlinear monotone equations, J. Ind. Manag. Optim., 13 (2017), 283-295.
J. Liu and Y. Feng, A derivative-free iterative method for nonlinear monotone equations with convex constraints,Numer. Algor., 82 (2019), 245-262.
S.Y. Liu, Y.Y. Huang and H.W. Jiao, Sufficient descent conjugate gradient methods for solving convex constrined nonlinear monotone equations, Abstr. Appl. Anal., 2014 Article ID 305643 (2014), 12 pages.
Z. Liu, S. Du and R. Wang, A new conjugate gradient projection method for solving stochastic generalized linear complementarity problems, J. Appl. Math. Phys., 4 (2016), 1024-1031.
I.E. Livieris, V. Tampakas and P. Pintelas, A descent hybrid conjugate gradient method based on the memoryless BFGS update, Numer. Algor., 79(4) (2018), 1169-1185.
Y. Ou and J. Li, A new derivative-free SCG-type projection method for nonlinear monotone equations with convex constraints, J. Appl. Math. Comput., 56 (2018), $195-216$.
M.V. Solodov and B.F. Svaiter, A globally convergent inexact newton method for systems of monotone equations, In Fukushima M., Qi L. (eds) Reformulation: Nonsmooth,
Piecewise Smooth, Semismoothing methods, Applied Optimization, it J. (eds). Springer, Boston, MA, (1998), $355-369$.
P.S. Stanimirović, B. Ivanov, S. Djordjević and I. Brajević, New hybrid conjugate gradient and Broyden-FletcherGoldfarb-Shanno conjugate gradient methods, J. Optim. Theory. Appl., 178 (2018), 860-884.
C. Wang, Y. Wang and C. Xu, A projection method for a system of nonlinear monotone equations with convex constraints, Math. Meth. Oper. Res., 66 (2007), 33-46.
S. Wang and H. Guan, A scaled conjugate gradient method for solving monotone nonlinear equations with convex constraints, J. Appl. Math., 2013 Article ID 286486 (2013), 7 pages.
X.Y. Wang, S.J. Li and X.P. Kou, A self-adaptive threeterm conjugate gradient method for monotone nonlinear equations with convex constraints, Calcolo, 53 (2016), $133-145$.
Y. Xiao and H. Zhu, A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing, J. Math. Anal. Appl., 405 (2013), 310-319.
Y.B. Zhao and D.H. Li, Monotonicity of fixed point and normal mapping associated with variational inequality and its application, SIAM J. Optim., 11 (2001), 962-973.
L. Zheng, A modified PRP projection method for nonlinear equations with convex constraints, Int. J. Pure. Appl. Math., 79 (2012), 87-96 .
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