Abstract
A class of polynomial primal-dual interior-point algorithms for P ∗ (κ) linear complementarity problems (LCPs) are presented. We generalize Ghami et al.’s[A polynomial-time algorithm for linear optimization based on a new class of kernel functions(2008)] algorithm for linear optimization (LO) problem to P ∗ (κ) LCPs. Our analysis is based on a class of finite kernel functions which have the linear and quadratic growth terms. Since P*(κ) LCP is a generalization of LO problem, we lose the orthogonality of the vectors dx and ds. So our analysis is different from the one in Ghami et al’s algorithm. Despite this, the favorable complexity result is obtained, namely, \(O((1 + 2\kappa)n^{\frac{1}{1+p}}\log n \log(n/\epsilon))\), which is better than the usual large-update primal-dual algorithm based on the classical logarithmic barrier function for P ∗ (κ) LCP.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bullups, S.C., Murty, K.G.: Complementarity problems. J. Comput. Appl. Math. 124, 303–318 (2000)
Cho, G.M.: A new large-update interior point algorithm for P*(κ) linear complementarity problems. J. Comput. Appl. Math. 216, 265–278 (2008)
Cho, G.M., Kim, M.K.: A new lerge-update interior-piont algorithm for P*(κ) LCPs based on kernel finction. Appl. Math. Comput. 182, 1169–1183 (2006)
Cho, G.M., Kim, M.K., Lee, Y.H.: Complexity of large-update interior point algorithm for P*(κ) linear complementarity problem. Comput. Math. Appl. 53, 948–960 (2007)
Illés, T., Nagy, M.: The Mizuno - Todd - Ye predictor - corrector algorithm for sufficient matrix linear complementarity problem. European J. Oper. Res. 181, 1097–1111 (2007)
El Ghami, M., Ivanov, I., Melissen, J.B.M., Roos, C., Steihaug, T.: A polynomial-time algorithm for linear optimization based on a new class of kernel functions. J. Comput. Appl. math. (2008), http://www.sciencedirect.com
Kojima, M., Megiddo, N., Noma, T., Yoshise, A.: A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems. LNCS, vol. 538. Springer, Heidelberg (1991)
A new efficient large-update primal-dual interior-point method based on a finite barrier. SIAM. J. Optim. 13, 766–782 (2003)
Bai, Y.Q., EI Ghami, M., Roos, C.: A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization. SIAM. J. Optim. 15, 101–128 (2004)
Peng, J., Roos, C., Terlaky, T.: Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms. Princeton University Press, USA (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, H., Zhang, M., Zhao, Y. (2009). A Class of New Large-Update Primal-Dual Interior-Point Algorithms for \(\emph{P}_\ast(\kappa)\) Linear Complementarity Problems. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5553. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01513-7_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-01513-7_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01512-0
Online ISBN: 978-3-642-01513-7
eBook Packages: Computer ScienceComputer Science (R0)