A Regularized Smoothing Newton Method for Symmetric Cone Complementarity Problems

This paper extends the regularized smoothing Newton method in vector optimization to symmetric cone optimization, which provide a unified framework for dealing with the nonlinear complementarity problem, the second-order cone complementarity problem, and the semidefinite complementarity problem (SCCP). In particular, we study strong semismoothness and Jacobian nonsingularity of the total natural residual function and show that the algorithm of Hayashi, Yamashita and Fukushima [SIAM J. Optim., 15 (2005), pp. 593-615] for the monotone SOCCP can be extended to the monotone SCCP.