TWO METHODS FOR FINDING A SPARSE SOLUTION OF THE LINEAR COMPLEMENTARITY PROBLEM WITH Z-MATRIX

In this paper, we propose two numerical methods to find a sparse solution of the linear complementarity problem (LCP) with a Z-matrix. The first one is an iterative method besed on solving the lower-dimensional linear equations by using Gaussian elimination, which terminates at a sparsest solution of the LCP within a finite number of iterations, and the computational complexity of the method is O(mu(3)) where mu is the number of non-zero elements in the sparsest solution of the LCP. The second one is a fixed point iterative method starting from a feasible point of the LCP, which converges monotonically downward to a solution of the LCP, and specially, it can be used to find a sparse solution of the LCP if the starting point is sparse. Compared with several existing methods, the numerical results show the advantage and the effectiveness of the proposed methods.