Limiting behavior of trajectories generated by a continuation method for monotone complementarity problems

Defining the mapping F from the 2n-dimensional Euclidean space into itself by for every , the authors write the CP, the complementarity problem, with a mapping as the system of equations and , where denotes the nonnegative orthant of . Under the assumption that f is a monotone function on , they show that F maps the positive orthant of homeomorphically. This result then ensures the existence of a trajectory consisting of the solutions of the system of equations and where w is a continuous mapping from the unit interval [0, 1] into such that ; if t=0, the system coincides with the CP. The authors study limiting behavior of the trajectory as , and give some sufficient conditions for the trajectory to lead to a solution of the CP. This approach is an extension of the one used in the polynomially bounded algorithm recently given by Kojima, Mizuno and Yoshise for solving positive semidefinite linear complementarity problems.