Recently, [Y.Q. Bai, M. El Ghami and C. Roos, SIAM J. Opt. 15 (2004) 101–128] investigated a new class of kernel functions which differs from the class of self-regular kernel functions. The class is defined by some simple conditions on the growth and the barrier behavior of the kernel function. In this paper we generalize the analysis presented in the above paper for P*(κ) Linear Complementarity Problems (LCPs). The analysis for LCPs deviates significantly from the analysis for linear optimization....