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Articles

On perturbation bounds of the linear complementarity problem

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Pages 625-638 | Received 22 Jul 2016, Accepted 15 Mar 2017, Published online: 10 Apr 2017

References

  • Cottle RW, Pang JS, Stone RE. The linear complementarity problem. San Diego: Academic Press; 1992.
  • Ferris MC, Pang JS. Engineering and economic applications of complementarity problems. SIAM Rev. 1997;39:669–713.
  • van Bokhoven WMG. Piecewise-linear modelling and analysis. Proefschrift: Eindhoven; 1981.
  • Bai ZZ. Modulus-based matrix splitting iteration methods for linear complementarity problems. Numer Linear Algebra Appl. 2010;17:917–933.
  • Bai ZZ, Zhang LL. Modulus-based synchronous multisplitting iteration methods for linear complementarity problems. Numer Linear Algebra Appl. 2013;20:425–439.
  • Bai ZZ, Zhang LL. Modulus-based synchronous two-stage multisplitting iteration methods for linear complementarity problems. Numer Algorithms. 2013;62:59–77.
  • Li W. A general modulus-based matrix splitting method for linear complementarity problems of H-matrices. Appl Math Lett. 2013;26:1159–1164.
  • Liu SM, Zheng H, Li W. A general accelerated modulus-based matrix splitting iteration method for solving linear complementarity problems. Calcolo. 2016;53:189–199.
  • Zhang LL. Two-step modulus based matrix splitting iteration for linear complementarity problems. Numer Algorithms. 2011;57:83–99.
  • Zhang LL. Two-stage multisplitting iteration methods using modulus-based matrix splitting as inner iteration for linear complementarity problems. J Optim Theory App. 2014;160:189–203.
  • Zhang LL. Two-step modulus-based synchronous multisplitting iteration methods for linear complementarity problems. J Comput Math. 2015;33:100–112.
  • Zheng H, Li W. The modulus-based nonsmooth Newton’s method for solving linear complementarity problems. J Comput App Math. 2015;288:116–126.
  • Li W, Zheng H. A preconditioned modulus-based iteration method for solving linear complementarity problems of H-matrices. Linear Multilinear Algebra. 2016;64:1390–1403.
  • Zheng H, Li W, Vong SW. A relaxation modulus-based matrix splitting iteration method for solving linear complementarity problems. Numer Algorithms. 2017;74:137–152.
  • Zheng N, Yin JF. Accelerated modulus-based matrix splitting iteration methods for linear complementarity problems. Numer Algorithms. 2013;64:245–262.
  • Chen TT, Li W, Wu XP, et al. Error bounds for linear complementarity problems of MB-matrices. Numer Algorithms. 2015;70(2):341–356.
  • Chen XJ, Xiang SH. Computation of error bounds for P-matrix linear complementarity problems. Math Program Ser A. 2006;106:513–525.
  • Garcia-Esnaola M, Peña JM. A comparison of error bounds for linear complementarity problems of H-matrices. Linear Algebra Appl. 2010;433:956–964.
  • Li W, Zheng H. Some new error bounds for linear complementarity problems of H-matrices. Numer Algorithms. 2014;67:257–269.
  • Chen XJ, Xiang SH. Perturbation bounds for P-matrix linear complementarity problems. SIAM J Optim. 2007;18(4):1250–1265.
  • Berman A, Plemmons RJ. Nonnegative matrices in the mathematical sciences. Philadelphia: SIAM Publisher; 1994.
  • Golub GH, van Loan CF. Matrix computation. 4th ed. Baltimore: Johns Hopkins University Press; 2013.
  • Kakimura N. Sign-solvable linear complementarity problems. Linear Algebra Appl. 2008;429:606–616.
  • Dong JL, Jiang MQ. A modified modulus method for symmetric positive-definite linear complementarity problems. Numer Linear Algebra Appl. 2009;16:129–143.

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