A complementarity problem with a continuous mapping f from Rn into itself can be written as the system of equations F(x,y)=0 and (x,y)≥0. Here F is the mapping from R2n into itself defined by F(x,y)=(x1y1,x2y2,...,xnyn,y-f(x)). Under the assumption that the mapping f is a P0-function, the authors study various aspects of homotopy continuation methods that trace a trajectory consisting of solutions of the family of systems of equations F(x,y)=t(a,b) and (x,y)≥0 until the parameter t≥0 attains 0. Here (a,b) denotes a 2n-dimensional constant positive vector. The authors establish the existence of a trajectory which leads to a solution of the problem, and then present a numerical method for tracing the trajectory. They also discuss the global and local convergence of the method.
