New kernel function with parametrized default step size for linear complementarity problem

Abstract

Defining new search directions for primal-dual interior-point algorithm for solving linear complementarity problems mainly depends on kernel
functions. In this paper, we introduce a new logarithmic kernel function with
double barrier term and two parameters, the first one uses to determine the
best complexity for the large-update primal-dual IPMs, whereas the second
one uses to control the default step size. These results are the best known
complexity bound for large-update with a logarithmic boundary term. At
last, we report some numerical results to show the practical performance of
the proposed algorithm with different parameters.