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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∗(κ)Open image in new window-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.

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