A power penalty method for second-order cone nonlinear complementarity problems

A power penalty method for solving nonlinear second-order cone complementarity problems (SOCCPs) is proposed. By using this method, the nonlinear SOCCP is converted to asymptotic nonlinear equations. The merit of this method shows that the solution sequence of the asymptotic nonlinear equations converges to the solution of the nonlinear SOCCP at an exponential rate when the penalty parameter tends to positive infinity under mild assumptions. An algorithm is constructed and numerical examples indicate the feasibility of our method.