199
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

A globally convergent projection method for a system of nonlinear monotone equations

&
Pages 719-737 | Received 02 Dec 2019, Accepted 23 May 2020, Published online: 09 Jun 2020

References

  • A.B. Abubakar and P. Kumam, A descent Dai-Liao conjugate gradient method for nonlinear equations, Numer. Algor. 81 (2019), pp. 197–210. doi: 10.1007/s11075-018-0541-z
  • A.B. Abubakar, P. Kumam, and A.M. Awwal, A descent Dai-Liao projection method for convex constrained nonlinear monotone equations with applications, Thai J. Math. 2018 (2019), pp. 128–152. Special Issue: Annual Meeting in Mathematics.
  • 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 (2019), p. 767. doi:10.3390/math7090767.
  • W. Cruz and M. Raydan, Nonmonotone spectral methods for large-scale nonlinear systems, Optim. Methods Softw. 18 (2003), pp. 583–599. doi: 10.1080/10556780310001610493
  • W. Cruz, J.M. Martinez, and M. Raydan, Spectral residual method without gradient information for solving large-scale nonlinear systems of equations, Math. Comput. 75(255) (2006), pp. 1429–1448. doi: 10.1090/S0025-5718-06-01840-0
  • Y.H. Dai and Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim. 10 (1999), pp. 177–182. doi: 10.1137/S1052623497318992
  • E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles, Math. Program. 91 (2002), pp. 201–213. doi: 10.1007/s101070100263
  • P. Gao and C. He, An effecient three-term conjugate gradient method for nonlinear monotone equations with convex constraints, Calcolo 55 (2018), p. 53. Available at https://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), pp. 1–16. doi: 10.1016/j.cam.2019.03.018
  • 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 (2019), Article ID 5261830, 17 pages.
  • M. Hassan and M.Y. Waziri, On Broyden-like update via some quadratures for solving nonlinear systems of equations, Turk. J. Math. 39 (2015), pp. 335–345. doi: 10.3906/mat-1404-41
  • A.N. Iusem, M.V. Solodov, Newton-type methods with generalized distances for constrained optimization. Optim. 41 (1997), pp. 257–278. doi: 10.1080/02331939708844339
  • C. Kanzow, N. Yamashita, and M. Fukushima, Levenberg-Marquardt methods for constrained nonlinear equations with strong local convergence properties, J. Comput. Appl. Math. 172 (2004), pp. 375–397. doi: 10.1016/j.cam.2004.02.013
  • M. Koorapetse and P. Kaelo, Globally convergent three-term conjugate gradient projection methods for solving nonlinear monotone equations, Arab. J. Math. (Springer) 7 (2018), pp. 289–301. doi: 10.1007/s40065-018-0206-8
  • 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), pp. 755–770. doi: 10.1007/s41980-018-0163-1
  • M. Li, H. Liu, and Z. Liu, A new family of conjugate gradient methods for unconstrained optimization, J. Appl. Math. Comput. 58 (2018), pp. 219–234. doi: 10.1007/s12190-017-1141-0
  • J.K. Liu and X.L. Du, A gradient projection method for the sparse signal reconstruction in compressive sensing, Appl. Anal. 97(12) (2018), pp. 2122–2131. doi: 10.1080/00036811.2017.1359556
  • J. Liu and S. Du, Modified three-term conjugate gradient method and its applications, Math. Prob. Eng. 2019 (2019), Article ID 5976595, 9 pages.
  • J. Liu and Y. Feng, A derivative-free iterative method for nonlinear monotone equations with convex constraints, Numer. Algor. 82 (2019), pp. 245–262. doi: 10.1007/s11075-018-0603-2
  • J.K. Liu and S.J. Li, A three-term derivative-free projection method for nonlinear monotone system of equations, Calcolo 53 (2016), pp. 427–450. doi: 10.1007/s10092-015-0156-x
  • B. Mahdad and K. Srairi, Optimal power flow improvement using hybrid teaching-learning-based optimization and pattern search, Int. J. Mod. Educ. Comput. Sci. 10 (2018), pp. 55–70. doi: 10.5815/ijmecs.2018.03.07
  • H. Mohammad and A.B. Abubakar, A positive spectral gradient-like method for large-scale nonlinear monotone, Bull. Comput. Appl. Math. 5(1) (2017), pp. 99–115.
  • M.V. Solodov, B.F. Svaiter, A globally convergent inexact Newton method for systems of monotone equations, In: Fukushima M., Qi L. (eds) Reformulation: Nonsmooth, Semismooth and Smoothing Methods, Applied Optimization, 22, Springer, Boston, MA, 1998, pp. 355–369.
  • M. Sun and J. Liu, Three derivative-free projection methods for nonlinear equations with convex constraints, J. Appl. Math. Comput. 47 (2015), pp. 265–276. doi: 10.1007/s12190-014-0774-5
  • Z. Wan, Z. Yang, and Y. Wang, New spectral PRP conjugate gradient method for unconstrained optimization, Appl. Math. Lett. 24(1) (2011), pp. 16–22. doi: 10.1016/j.aml.2010.08.002
  • M.Y. Waziri, W.J. Leong, M.A. Hassan, and M. Monsi, A new Newton's method with diagonal jacobian approximation for systems of nonlinear equations, J. Math. Stat. 6 (2010), pp. 246–252. doi: 10.3844/jmssp.2010.246.252
  • Z. Yu, J. Lin, J. Sun, Y. Xiao, L. Liu, and Z. Li, Spectral gradient projection method for monotone nonlinear equations with convex constraints, Appl. Numer. Math. 59 (2009), pp. 2416–2423. doi: 10.1016/j.apnum.2009.04.004
  • N. Yuan, A derivative-free projection method for solving convex constrained monotone equations, ScienceAsia 43 (2017), pp. 195–200. doi: 10.2306/scienceasia1513-1874.2017.43.195
  • G. Yuan and M. Zhang, A three-terms Polak-Ribière-Polyak conjugate gradient algorithm for large-scale nonlinear equations, J. Comput. Appl. Math. 286 (2015), pp. 186–195. doi: 10.1016/j.cam.2015.03.014
  • G. Yuan, S. Lu, and Z. Wei, A new trust region method with line search for solving symmetric nonlinear equations, Int. J. Comput. Math. 88 (2011), pp. 2109–2123. doi: 10.1080/00207160.2010.526206
  • G. Yuan, Z. Meng, and Y. Li, A modified Hestenes and Stiefel conjugate gradient algorithm for large-scale nonsmooth minimizations and nonlinear equations, J. Optim. Theory Appl. 168 (2016), pp. 129–152. doi: 10.1007/s10957-015-0781-1
  • G. Yuan, B. Wang, and Z. Sheng, The Hager-Zhang conjugate gradient algorithm for large-scale nonlinear equations, Int. J. Comput. Math. 96(8) (2019), pp. 1533–1547. doi: 10.1080/00207160.2018.1494825
  • L. Zhang and W. Zhou, Spectral gradient projection method for solving nonlinear monotone equations, J. Comput. Appl. Math. 196 (2006), pp. 478–484. doi: 10.1016/j.cam.2005.10.002
  • Y.B. Zhao and D. Li, Monotonicity of fixed point and normal mappings associated with variational inequality and its application, SIAM J. Optim. 11 (2001), pp. 962–973. doi: 10.1137/S1052623499357957

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.