Kernel function based interior-point methods for horizontal linear complementarity problems

It is well known that each kernel function defines an interior-point algorithm. In this paper we propose new classes of kernel functions whose form is different from known kernel functions and define interior-point methods (IPMs) based on these functions whose barrier term is exponential power of exponential functions for P*(kappa)-horizontal linear complementarity problems (HLCPs). New search directions and proximity measures are defined by these kernel functions. We obtain so far the best known complexity results for large-and small-update methods.