中文摘要：

利用同伦方法求解线性互补问题,通过对R0矩阵对应的线性互补问题构造新同伦方程,给出同伦路径存在的一个新条件,并在该条件下证明同伦路径的有界性和收敛性,得到了线性互补问题解存在的一个条件.

英文摘要：

We used the homotopy method to solve the linear complementarity problem. By constructing a new homotopy equation for the linear complementarity problem corresponding to the R0-matrix, we gave a new condition for the existence of homotopy path. Under this condition, we proved the boundedness and convergence of the homotopy path, and obtained a condition for the existence of a solution of the linear complementarity problem.