NEW COMPLEXITY ANALYSIS OF PRIMAL-DUAL IMPS FOR P* LAPS BASED ON LARGE UPDATES

Title & Authors
NEW COMPLEXITY ANALYSIS OF PRIMAL-DUAL IMPS FOR P* LAPS BASED ON LARGE UPDATES
Cho, Gyeong-Mi; Kim, Min-Kyung;

Abstract
In this paper we present new large-update primal-dual interior point algorithms for $\small{P_*}$ linear complementarity problems(LAPS) based on a class of kernel functions, ${\psi}(t) Keywords primal-dual interior point method;kernel function;complexity;polynomial algorithm;large-update;linear complementarity;path-following; Language Korean Cited by References 1. Y. Q. Bai, M. El Ghami, and C. Roos, A new efficient large-update primal-dual interiorpoint method based on a finite barrier, SIAM J. Optim. 13 (2002), no. 3, 766–782 2. Y. Q. Bai, M. El Ghami, and C. Roos, A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization, SIAM J. Optim. 15 (2004), no. 1, 101–128 3. G. M. Cho, M. K. Kim, and Y. H. Lee, Complexity of large-update interior point algorithm for$P_*(\kappa)$linear complementarity problems, Comput. Math. Appl. 53 (2007), no. 6, 948–960 4. M. El Ghami, I. Ivanov, J. B. M. Melissen, C. Roos, and T. Steihaug, A polynomial-time algorithm for linear optimization based on a new class of kernel functions, Journal of Computational and Applied Mathematics, DOI 10.1016/j.cam.2008.05.027 5. T. Illes and M. Nagy, A Mizuno-Todd-Ye type predictor-corrector algorithm for sufficient linear complementarity problems, European J. Oper. Res. 181 (2007), no. 3, 1097–1111 6. M. Kojima, N. Megiddo, T. Noma, and A. Yoshise, A primal-dual interior point algorithm for linear programming, Progress in mathematical programming (Pacific Grove, CA, 1987), 29–47, Springer, New York, 1989 7. M. Kojima, N. Megiddo, T. Noma, and A. Yoshise, A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems, Lecture Notes in Computer Science, 538. Springer-Verlag, Berlin, 1991 8. M. Kojima, S. Mizuno, and A. Yoshise, A polynomial-time algorithm for a class of linear complementarity problems, Math. Programming 44 (1989), no. 1, (Ser. A), 1–26 9. M. Kojima, S. Mizuno, and A. Yoshise, An O($\sqrt{n}$L) iteration potential reduction algorithm for linear complementarity problems, Math. Programming 50 (1991), no. 3, (Ser. A), 331–342 10. N. Megiddo, Pathways to the optimal set in linear programming, Progress in mathematical programming (Pacific Grove, CA, 1987), 131–158, Springer, New York, 1989 11. J. Miao, A quadratically convergent O(($\kappa + 1)\sqrt{n}$L)-iteration algorithm for the$P_*(\kappa)\$-matrix linear complementarity problem, Math. Programming 69 (1995), no. 3, Ser. A, 355–368

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