A regularization method for the second - order cone complementarity problem with the Cartesian P 0 - property

We consider the Tikhonov regularization method for the second-order cone complementarity problem (SOCCP) with the Cartesian P0-property. We show that many results of the regularization method for the P0 nonlinear complementarity problem still hold for this important class of nonmonotone SOCCP. For example, under the more general setting, every regularized problem has a unique optimal solution, and the solution trajectory generated is bounded when the original SOCCP has a nonempty and bounded solution set. We also propose an inexact regularization algorithm by solving the sequence of regularized problems approximately with the merit function approach based on Fischer-Burmeister merit function, and establish the convergence result of the algorithm. Preliminary numerical results are also reported, which verify the favorable theoretical property of the proposed method.