Free Access
Issue
RAIRO-Oper. Res.
Volume 54, Number 2, March-April 2020
Page(s) 341 - 349
DOI https://doi.org/10.1051/ro/2019002
Published online 27 February 2020
  • K.G. Murty, Linear Complementarity, Linear and Nonlinear Programming. Heldermann Verlag, Berlin (1988). [Google Scholar]
  • M.S. Bazaraa, H.D. Sheral and C.M. Shetty, Nonlinear Programming, Theory and Algorithms, 3rd edition. Wiley-Interscience, Hoboken, NJ (2006). [CrossRef] [Google Scholar]
  • R.W. Cottle, J.S. Pang and R.E. Stone, The Linear Complementarity Problem. Academic Press, London (1992). [Google Scholar]
  • Z.Z. Bai and D.J. Evans, Matrix multisplitting relaxation methods for linear complementarity problems. Int. J. Comput. Math. 63 (1997) 309–326. [Google Scholar]
  • D. Yuan and Y.Z. Song, Modified AOR methods for linear complementarity problem. Appl. Math. Comput. 140 (2003) 53–67. [Google Scholar]
  • L. Cvetkovi, S. Rapaji, How to improve MAOR method convergence area for linear complementarity problems. Appl. Math. Comput. 162 (2005) 577–584. [Google Scholar]
  • Y. Li and P. Dai, Generalized AOR methods for linear complementarity problem. Appl. Math. Comput. 188 (2007) 7–18. [Google Scholar]
  • M.H. Xu and G.F. Luan, A rapid algorithm for a class of linear complementarity problems. Appl. Math. Comput. 188 (2007) 1647–1655. [Google Scholar]
  • M. Dehghan and M. Hajarian, Convergence of SSOR methods for linear complementarity problems. Oper. Res. Lett. 37 (2009) 219–223. [CrossRef] [Google Scholar]
  • H. Saberi, S. Najafi, A. Edalatpanah, On the two SAOR iterative formats for solving linear complementarity problems. I.J. Inf. Technol. Comput. Sci. 3 (2011) 19–24. [Google Scholar]
  • H. Saberi, S. Najafi and A. Edalatpanah, A kind of symmetrical iterative methods to solve special class of LCP (#). Int. J. Appl. Math. App. 4 (2012) 183–189. [Google Scholar]
  • H. Saberi, S. Najafi and A. Edalatpanah, On the convergence regions of generalized accelerated overrelaxation method for linear complementarity problems. J. Optim. Theory Appl. 156 (2013) 859–866. [Google Scholar]
  • L.T. Zhang, X.Y. Zuo, T.X. Gu and X.P. Liu, Improved convergence theorems of multisplitting methods for the linear complementarity problem. Appl. Math. Comput. 243 (2014) 982–987. [Google Scholar]
  • A. Hadjidimos and M. Tzoumas, On the solution of the linear complementarity problem by the generalized accelerated overrelaxation iterative method. J. Optim. Theory Appl. 165 (2015) 545–562. [Google Scholar]
  • A. Hadjidimos and M. Tzoumas, The solution of the linear complementarity problem by the matrix analogue of the accelerated overrelaxation iterative method. Numer. Algor. 73 (2016) 665–684. [CrossRef] [Google Scholar]
  • A. Hadjidimos and L.L. Zhang, Comparison of three classes of algorithms for the solution of the linear complementarity problem with an H+-matrix. J. Comput. Appl. Math. 336 (2018) 175–191. [Google Scholar]
  • W.M.G. van Bokhoven, A Class of Linear Complementarity Problems is Solvable in Polynomial Time. Department of Electrical Engineering, University of Technology, Eindhoven, Netherlands (1980). [Google Scholar]
  • J.-L. Dong and M.-Q. Jiang, A modified modulus method for symmetric positive-definite linear complementarity problems. Numer. Linear Algebra Appl. 16 (2009) 129–143. [Google Scholar]
  • Z.-Z. Bai, Modulus-based matrix splitting iteration methods for linear complementarity problems. Numer. Linear Algebra Appl. 17 (2010) 917–933. [Google Scholar]
  • L.-L. Zhang and Z.-R. Ren, Improved convergence theorems of modulus-based matrix splitting iteration methods for linear complementarity problems. Appl. Math. Lett. 26 (2013) 638–642. [Google Scholar]
  • L.-L. Zhang, Y.-P. Zhang and Z.-R. Ren, New convergence proofs of modulus-based synchronous multisplitting iteration methods for linear complementarity problems. Linear Algebra Appl. 481 (2015) 83–93. [Google Scholar]
  • S. Liu, H. Zheng and W. Li, A general accelerated modulus-based matrix splitting iteration method for solving linear complementarity problems. Calcolo 53 (2016) 189–199. [CrossRef] [Google Scholar]
  • H. Zheng, W. Li and S. Vong, A relaxation modulus-based matrix splitting iteration method for solving linear complementarity problems. Numer. Algorithms 74 (2017) 137–152. [Google Scholar]
  • H. Saberi Najafi and S.A. Edalatpanah, Verification of iterative methods for the linear complementarity problem: verification of iterative methods for LCPs, edited by P. Vasant, G. Weber and V. Dieu. In: Handbook of Research on Modern Optimization Algorithms and Applications in Engineering and Economics. IGI Global, Hershey, PA (2016) 545–580. [CrossRef] [Google Scholar]
  • C.Y. Liu and C.L. Li, A new preconditioned Generalized AOR methods for the Linear complementarity problem based on a generalized Hadjidimos preconditioner. East Asian J. Appl. Math. 2 (2012) 94–107. [CrossRef] [Google Scholar]
  • B.X. Duan, W.Y. Zeng and X.P. Zhu, A preconditioned Gauss-Seidel iterative method for linear complementarity problem in intelligent materials system. Adv. Mater. Res. 340 (2012) 3–8. [CrossRef] [Google Scholar]
  • Y. Liu, R. Zhang, Y. Wang and X. Huang, Comparison analysis on preconditioned GAOR method for linear complementarity problem. J. Inf. Comput. Sci. 9 (2012) 4493–4500. [Google Scholar]
  • H. Saberi Najafi and S.A. Edalatpanah, Iterative methods with analytical preconditioning technique to linear complementarity problems: application to obstacle problems. RAIRO-Oper. Res. 47 (2013) 59–71. [CrossRef] [EDP Sciences] [Google Scholar]
  • C. Liu and C.L. Li, A preconditioned multisplitting and Schwarz method for linear complementarity problem. J. Appl. Math. 519017 (2014) 6. [Google Scholar]
  • R.S. Varga, Matrix Iterative Analysis, 2nd edition. Springer, Berlin (2000). [CrossRef] [Google Scholar]
  • A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York, NY (1979). [Google Scholar]
  • M. Hazewinkel, Monomial Representation. Encyclopedia of Mathematics, Springer (2001). [Google Scholar]
  • O. Ore, Theory of monomial groups. Trans. Am. Math. Soc. 51 (1942) 15–64. [Google Scholar]

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