A Regularization Smoothing Newton Method for the Symmetric Cone Complementarity Problem with the Cartesian P0-property

Abstract

In this paper, we consider the symmetric cone linear complementarity problem with the Cartesian P₀-property and present a regularization smoothing method with a nonmonotone line search to solve this problem. It has been demonstrated that the proposed method exhibits global convergence under the condition that the solution set of the complementarity problem is nonempty. This condition is less stringent than those that have appeared in some existing literature. We also show that the method has locally quadratic convergence under appropriate conditions. Some experimental results are reported to illustrate the efficiency of the proposed method.