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A numerical embedding method was proposed for solving the nonlinear optimization problem. By using the nonsmooth theo-ry, the existence and the continuation of the following path for the corresponding homotopy equations were proved. Therefore the ba-sic theory for the algorithm of the numerical embedding method for solving the non-linear optimization problem was established. Basedon the theoretical results, a numerical embedding algorithm was designed for solving the nonlinear optimization problem, and prove itsconvergence carefully. Numerical experiments show that the algorithm is effective.