Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 67, 2018 - Issue 9: International Workshop on Nonlinear and Variational Analysis 2017
76
Views
1
CrossRef citations to date
0
Altmetric
General Articles

Iterative complexities of a class of homogeneous algorithms for monotone nonlinear complementarity problems over symmetric cones

&
Pages 1505-1521 | Received 18 May 2016, Accepted 14 Apr 2018, Published online: 17 Jun 2018

References

  • Faybusovich L. Linear systems in Jordan algebras and primal-dual interior-point algorithms. J Comput Appl Math. 1997;86(1):149–175. doi: 10.1016/S0377-0427(97)00153-2
  • Luo Z, Xiu N. An infeasible interior-point algorithm for symmetric cone LCP via CHKS function. Acta Appl Math. 2009;25:593–606. doi: 10.1007/s10255-008-8814-2
  • Luo Z, Xiu N. Path-following interior point algorithms for the Cartesian -LCP over symmetric cones. SCI China Ser A. 2009;52:1769–1784. doi: 10.1007/s11425-008-0174-0
  • Lesaja G, Roos C. Kernel-based interior-point methods for monotone linear complementarity problems over symmetric cones. J Optim Theory Appl. 2011;150(3):444–474. doi: 10.1007/s10957-011-9848-9
  • Wang G, Bai Y. A class of Polynomial interior point algorithms for the Cartesian P-matrix linear complementarity problem over symmetric cones. J Optim Theory Appl. 2012;152:739–772. doi: 10.1007/s10957-011-9938-8
  • Lesaja G, Wang G, Zhu D. Interior-point methods for Cartesian linear complementarity problems over symmetric cones based on the eligible kernel functions. Optim Methods Softw. 2012;27(4-5):827–843. doi: 10.1080/10556788.2012.670858
  • Asadi S, Mansouri H, Darvay Zs, et al. On the horizontal linear complementarity problems over Cartesian product of symmetric cones. Optim Method Softw. 2016;31(2):233–257. doi: 10.1080/10556788.2015.1058795
  • Asadi S, Mansouri H, Darvay Zs. An infeasible full-NT step IPM for horizontal linear complementarity problem over Cartesian product of symmetric cones. Optimization. 2017;66(2):225–250. doi: 10.1080/02331934.2016.1267732
  • Kong L, Sun J, Xiu N. A regularized smoothing Newton method for symmetric cone complementarity problems. SIAM J Optim. 2008;19:1028–1047. doi: 10.1137/060676775
  • Zhao H, Liu H. Infeasible path-following interior point algorithm for Cartesian nonlinear complementarity problems over symmetric cones. Int J Comput Math. 2018;95(5):845–869. doi: 10.1080/00207160.2017.1297803
  • Liu X, Liu H, Wang W. Polynomial convergence of Mehrotra-type predictor-corrector algorithm for the Cartesian -LCP over symmetric cones. Optimization. 2013;64(4):1–23.
  • Rangarajan B. Polynomial convergence of infeasible-interior-point methods over symmetric cones. SIAM J Optim. 2006;16:1211–1229. doi: 10.1137/040606557
  • Yoshise A. Complementarity problems over symmetric cones: a survey of recent developments in several aspects. In: Anjos M.F., Lasserre J.B., editors. Handbook on semidefinite, coinc and polynomial optimization. New York (NY): Springer; 2012. ISBN 978-1-4614-0768-3
  • Zhao H, Liu H. A new infeasible Mehrotra-type predictor-corrector algorithm for nonlinear complementarity problems over symmetric cones. J Optim Theory Appl. 2018;176(2):410–427. doi: 10.1007/s10957-017-1194-0
  • Zhao H, Liu H. Infeasible Mehrotra-type predictor-corrector algorithm for cartesian nonlinear complementarity problems over symmetric cones. Int J Comput Math. 2018. doi:10.1080/00207160.2018.1429597.
  • Yoshise A. Interior point trajectories and a homogeneous model for nonlinear complementarity problem over symmetric cones. SIAM J Optim. 2006;17:1129–1153. doi: 10.1137/04061427X
  • Andersen E, Ye Y. On a homogeneous algorithm for the monotone complementarity problems. Math Program. 1999;84:375–400. doi: 10.1007/s101070050027
  • Yoshise A. Homogenous algorithms for monotone complementarity problems over symmetric cones. Pac J Optim. 2008;5(2):313–337.
  • Faraut J, Korányi A. Analysis on symmetric cone. New York (NY): Oxford University Press; 1994.
  • Schmieta S, Alizadeh F. Extension of primal-dual interior-point algorithm to symmetric cones. Math Program. 2003;96:409–438. doi: 10.1007/s10107-003-0380-z
  • Muramatsu M. On commutative class of search directions for linear programming over symmetric cones. J Optim Theory Appl. 2002;112:595–625. doi: 10.1023/A:1017920200889

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.