A generalized smoothing Newton method for the symmetric cone complementarity problem

In this paper, a concept of regulation functions is proposed, and some related properties and examples are explored. Based on this regulation function and some smoothing complementarity functions, we present a family of smoothing Newton methods to solve the symmetric cone complementarity problem. This algorithm allows a unified convergence analysis for some smoothing Newton methods. We show that the resulting Newton equation is well-defined and solvable, and provides a theory of global convergence.