A Smoothing Newton Algorithm for a Class of Non-monotonic Symmetric Cone Linear Complementarity Problems

Recently, the study of symmetric cone complementarity problems has been a hot topic in the literature. Many numerical methods have been proposed for solving such a class of problems. Among them, the problems concerned are generally monotonic. In this paper, we consider symmetric cone linear complementarity problems with a class of non‐monotonic transformations. A smoothing Newton algorithm is extended to solve this class of non‐monotonic symmetric cone linear complementarity problems; and the algorithm is proved to be well‐defined. In particular, we show that the algorithm is globally and locally quadratically convergent under mild assumptions. The preliminary numerical results are also reported.