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An Infeasible Interior-point Algorithm for Monotone Linear Complementarity Problems

Year 2021, Volume: 4 Issue: 2, 53 - 59, 31.12.2021

Welid Grimes , Mohamed Achache

https://doi.org/10.53508/ijiam.1036022
https://izlik.org/JA55HP49EL

Abstract

In this study, we implement a variant of infeasible interior-point algorithm for solving monotone linear complementarity problems (LCP). We first reformulate the monotone LCP as an minimization problem. Then a descent iterative method is applied to the latter. The descent direction is computed via the Newton method. However, for maintaining the positivity of iterates, a novel and efficient strategy is proposed. Some numerical results are reported to show the efficiency of our proposed approach.

Keywords

Monotone linear complementarity problems Newton method logarithmic penalty approach

References

  • Achache, M., Roumili, H., Keraghel, A.: A numerical study of an infeasible primal-dual path-following algorithm for linear programming. Applied Mathematics and Computation (186)(2), 1472--1479 (2007)
  • Cottle, R.W., Pang, J.S., and Stone, R.E.: The Linear Complementarity Problem. Academic Press, San Diego (1992)
  • Wright, S.J.: Primal-Dual Interior Point Methods. SIAM, Philadelphia, USA (1997)

Year 2021, Volume: 4 Issue: 2, 53 - 59, 31.12.2021

Welid Grimes , Mohamed Achache

https://doi.org/10.53508/ijiam.1036022
https://izlik.org/JA55HP49EL

Abstract

References

  • Achache, M., Roumili, H., Keraghel, A.: A numerical study of an infeasible primal-dual path-following algorithm for linear programming. Applied Mathematics and Computation (186)(2), 1472--1479 (2007)
  • Cottle, R.W., Pang, J.S., and Stone, R.E.: The Linear Complementarity Problem. Academic Press, San Diego (1992)
  • Wright, S.J.: Primal-Dual Interior Point Methods. SIAM, Philadelphia, USA (1997)
There are 3 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Review Article
Authors

Welid Grimes

Mohamed Achache This is me

Acceptance Date January 2, 2022
Publication Date December 31, 2021
DOI https://doi.org/10.53508/ijiam.1036022
IZ https://izlik.org/JA55HP49EL
Published in Issue Year 2021 Volume: 4 Issue: 2

Cite

APA Grimes, W., & Achache, M. (2021). An Infeasible Interior-point Algorithm for Monotone Linear Complementarity Problems. International Journal of Informatics and Applied Mathematics, 4(2), 53-59. https://doi.org/10.53508/ijiam.1036022
AMA 1.Grimes W, Achache M. An Infeasible Interior-point Algorithm for Monotone Linear Complementarity Problems. IJIAM. 2021;4(2):53-59. doi:10.53508/ijiam.1036022
Chicago Grimes, Welid, and Mohamed Achache. 2021. “An Infeasible Interior-Point Algorithm for Monotone Linear Complementarity Problems”. International Journal of Informatics and Applied Mathematics 4 (2): 53-59. https://doi.org/10.53508/ijiam.1036022.
EndNote Grimes W, Achache M (December 1, 2021) An Infeasible Interior-point Algorithm for Monotone Linear Complementarity Problems. International Journal of Informatics and Applied Mathematics 4 2 53–59.
IEEE [1]W. Grimes and M. Achache, “An Infeasible Interior-point Algorithm for Monotone Linear Complementarity Problems”, IJIAM, vol. 4, no. 2, pp. 53–59, Dec. 2021, doi: 10.53508/ijiam.1036022.
ISNAD Grimes, Welid - Achache, Mohamed. “An Infeasible Interior-Point Algorithm for Monotone Linear Complementarity Problems”. International Journal of Informatics and Applied Mathematics 4/2 (December 1, 2021): 53-59. https://doi.org/10.53508/ijiam.1036022.
JAMA 1.Grimes W, Achache M. An Infeasible Interior-point Algorithm for Monotone Linear Complementarity Problems. IJIAM. 2021;4:53–59.
MLA Grimes, Welid, and Mohamed Achache. “An Infeasible Interior-Point Algorithm for Monotone Linear Complementarity Problems”. International Journal of Informatics and Applied Mathematics, vol. 4, no. 2, Dec. 2021, pp. 53-59, doi:10.53508/ijiam.1036022.
Vancouver 1.Welid Grimes, Mohamed Achache. An Infeasible Interior-point Algorithm for Monotone Linear Complementarity Problems. IJIAM. 2021 Dec. 1;4(2):53-9. doi:10.53508/ijiam.1036022

International Journal of Informatics and Applied Mathematics