98
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

A smooth Newton method with 3-1 piecewise NCP function for generalized nonlinear complementarity problem

&
Pages 1703-1713 | Received 13 May 2016, Accepted 17 Apr 2017, Published online: 29 May 2017

References

  • B. Ahn, Iterative methods for linear complementarity problems with upperbounds and lowerbounds, Math. Program. 26 (1983), pp. 265–315.
  • R. Andreani, A. Friedlander, and S.A. Santos, On the resolution of the generalized nonlinear complementarity problem, SIAM J. Optim. 12(2) (2001), pp. 303–321. doi: 10.1137/S1052623400377591
  • J.S. Chen and S.H. Pan, A regularization semismooth Newton method based on the generalized Fischer-Burmeister function for P0-NCPs, J. Comput. Appl. Math. 220(1–2) (2008), pp. 464–479. doi: 10.1016/j.cam.2007.08.020
  • X. Chen, D. Sun, and L. Qi, Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities, Math. Comput. 67(222) (1998), pp. 519–541. doi: 10.1090/S0025-5718-98-00932-6
  • M.C. Ferris and J.S. Pang, Engineering and economic applications of complementarity problems, SIAM Rev. 39(4) (1997), pp. 669–713. doi: 10.1137/S0036144595285963
  • F. Francisco and J.S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Springer-Verlag, New York, 2003.
  • C. Geiger and C. Kanzow, On the resolution of monotone complementarity problems, Comput. Optim. Appl. 5(2) (1996), pp. 155–173. doi: 10.1007/BF00249054
  • J. Herskovits and S.R. Mazorche, A feasible directions algorithm for nonlinear complementarity problems and applications in mechanics, Struct. Multidiscip. Optim. 37(5) (2009), pp. 435–446. doi: 10.1007/s00158-008-0252-5
  • S.-L. Hu, Z.-H. Huang, and P. Wang, A nonmonotone smoothing Newton algorithm for solving nonlinear complementarity problems, Optim. Methods Softw. 24(3) (2009), pp. 447–460. doi: 10.1080/10556780902769862
  • X.H. Liu and T. Ni, Smoothing newton algorithm for solving generalized complementarity problem, Trans. Tianjin Univ. 16(1) (2010), pp. 75–79. doi: 10.1007/s12209-010-0014-5
  • A.L. Liu and D.G. Pu, 3-1 piecewise NCP function for new nonmonotone QP-free infeasible method, J. Robot. Mechatronics 26(5) (2014), pp. 566–572. doi: 10.20965/jrm.2014.p0566
  • T. Ni and P. Wang, A smoothing-type algorithm for solving nonlinear complementarity problems with a non-monotone line search, Appl. Math. Comput. 216 (2010), pp. 2207–2214.
  • H.-D. Qi and L.-Z. Liao, A smoothing newton method for general nonlinear complementarity problems, Comput. Optim. Appl. 17(2) (2000), pp. 231–253. doi: 10.1023/A:1026554432668
  • J.Y. Tang, L. Dong, J.C. Zhou, and L. Fang, A smoothing Newton method for nonlinear complementarity problems, Comput. Appl. Math. 32(1) (2013), pp. 107–118. doi: 10.1007/s40314-013-0015-9
  • J.Y. Tang, L. Dong, J.C. Zhou, and L. Sun, A smoothing-type algorithm for the second-order cone complementarity problem with a new nonmonotone line search, Optimization 64 (2015), pp. 1935–1955. doi: 10.1080/02331934.2014.906595
  • J.Y. Tang, J.C. Zhou, and L. Fang, A one-parametric class of smoothing functions and an improved regularization Newton method for the NCP, Optimization 65 (2016), pp. 977–1001. doi: 10.1080/02331934.2015.1105224
  • Y.J. Wang, F.M. Ma, and J.Z. Zhang, A nonsmooth L-M method for solving the generalized nonlinear complementarity problem, Appl. Math. Optim. 52(1) (2005), pp. 73–92. doi: 10.1007/s00245-005-0823-4
  • J. Zhang and K.C. Zhang, A variant smoothing Newton method for P0-NCP based on a new smoothing function, J. Comput. Appl. Math. 225(1) (2009), pp. 1–8. doi: 10.1016/j.cam.2008.06.012
  • X.Y. Zheng and J.R. Shi, Smoothing Newton method for generalized complementarity problems based on a new smoothing function, Appl. Math. Comput. 231 (2014), pp. 160–168.

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.