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