A Class of New Large-Update Primal-Dual Interior-Point Algorithms for $\emph{P}_\ast(\kappa)$ Linear Complementarity Problems

  • Authors:

  • Huaping Chen;Mingwang Zhang;Yuqin Zhao

  • Affiliations:

  • College of Science, China Three Gorges University, Yichang, China 443002;College of Science, China Three Gorges University, Yichang, China 443002;College of Science, China Three Gorges University, Yichang, China 443002

  • Venue:
  • ISNN 2009 Proceedings of the 6th International Symposium on Neural Networks: Advances in Neural Networks - Part III
  • Year:
  • 2009

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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.