NEW PRIMAL-DUAL INTERIOR POINT METHODS FOR P*(κ) LINEAR COMPLEMENTARITY PROBLEMS

Title & Authors
NEW PRIMAL-DUAL INTERIOR POINT METHODS FOR P*(κ) LINEAR COMPLEMENTARITY PROBLEMS
Cho, Gyeong-Mi; Kim, Min-Kyung;

Abstract
In this paper we propose new primal-dual interior point methods (IPMs) for $\small{P_*(\kappa)}$ linear complementarity problems (LCPs) and analyze the iteration complexity of the algorithm. New search directions and proximity measures are defined based on a class of kernel functions, $\psi(t) Keywords primal-dual interior point method;kernel function;complexity;polynomial algorithm;large-update;linear complementarity problem; Language English Cited by References 1. Y. Q. Bai, M. El Ghami, and C. Roos, A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization, SIAM J. Optim. 15 (2004), no. 1, 101–128. 2. Y. Q. Bai, J. Guo, and C. Roos, A new kernel function yielding the best known iteration bounds for primal-dual interior-point algorithms, Acta Math. Sin. (Engl. Ser.) 25 (2009), no. 12, 2169–2178. 3. G. M. Cho, M. K. Kim, and Y. H. Lee, Complexity of large-update interior point algorithm for$P_\ast(\kappa)$linear complementarity problems, Comput. Math. Appl. 53 (2007), no. 6, 948–960. 4. T. Illes and M. Nagy, A Mizuno-Todd-Ye type predictor-corrector algorithm for sufficient linear complementarity problems, European J. Oper. Res. 181 (2007), no. 3, 1097–1111. 5. M. Kojima, N. Megiddo, T. Noma, and A. Yoshise, A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems, Lecture Notes in Computer Science, 538. Springer-Verlag, Berlin, 1991. 6. M. Kojima, S. Mizuno, and A. Yoshise, A primal-dual interior point algorithm for linear programming, Progress in mathematical programming (Pacific Grove, CA, 1987), 29–47, Springer, New York, 1989. 7. M. Kojima, S. Mizuno, and A. Yoshise, A polynomial-time algorithm for a class of linear complementarity problems, Math. Programming 44 (1989), no. 1, (Ser. A), 1–26. 8. M. Kojima, S. Mizuno, and A. Yoshise, An O($\sqrt{n}L$) iteration potential reduction algorithm for linear complementarity problems, Math. Programming 50 (1991), no. 3, (Ser. A), 331–342. 9. N. Megiddo, Pathways to the optimal set in linear programming, Progress in mathematical programming (Pacific Grove, CA, 1987), 131–158, Springer, New York, 1989. 10. J. Miao, A quadratically convergent O(($\kappa$+ 1)$\sqrt{n}L$)-iteration algorithm for the$P_\ast(\kappa)\$- matrix linear complementarity problem, Math. Programming 69 (1995), no. 3, Ser. A, 355–368.

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