Primal-Dual Algorithms for P ∗(κ) Linear Complementarity Problems Based on Kernel-Function with Trigonometric Barrier Term

Abstract

AbstractRecently, El Ghami et al. [Journal of Computational and Applied Mathematics, May, 2011, doi:10.1016/j.cam.2011.05.036.] investigated a new kernel function which differs from the self-regular kernel functions. The kernel function has a trigonometric Barrier Term. In this paper we generalize the analysis presented in the above paper for P ∗(κ) Linear Complementarity Problems (LCPs). It is shown that the interior-point methods based on this function for large-update methods, the iteration bound is improved significantly. For small-update interior point methods the iteration bound is the best currently known bound for primal-dual interior point methods. The analysis for LCPs deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper.Key wordsInterior-pointKernel functionPrimal-dual methodLarge update, Small updateLinear complementarity problem