  In this article, we introduce a new homotopy function to trace the trajectory
by applying modified homotopy continuation method for finding the solution of
the linear complementarity problem. Earlier several authors attempted to
propose homotopy functions based on original problems. We propose the homotopy
function based on the Karush-Kuhn-Tucker condition of the corresponding
quadratic programming problem. The proposed approach extends the processability
of the larger class of linear complementarity problem and overcomes the
limitations of other existing homotopy approaches. We show that the homotopy
path approaching the solution is smooth and bounded with positive tangent
direction of the homotopy path. Various classes of numerical examples are
illustrated to show the effectiveness of the proposed algorithm and the
superiority of the algorithm among other existing iterative methods.
