Jian Jun Zhang ¹, De Ren Wang ¹

In this paper, we extend the numerical embedding method for solving the smooth equations to the nonlinear complementarity problem. By using the nonsmooth theory, we prove the existence and the continuation of the following path for the corresponding method for solving the nonlinear complementarity problem is established. In part II of this paper, we will further study the implementation of the method and give some numerical exapmles.

Key words: B-differentiable equations; Nonlinear complementarity problem; Nmerical embedding method.