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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. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce some concepts of E-properties for nonlinear transformations defined on Euclidean Jordan algebras, such as E-property, quad E-property, uniform Jordan E-property, E0-property. And then we study the implications among these E-properties. In particular, the quad E-property is equivalent to the E-property. The -copositive property implies the E0-property. The uniform Jordan E-property is proved to have the E0 and R0-properties. Based on the E-properties, we get some sufficient conditions to guarantee the solution existence for the nonlinear symmetric cone complementarity problem. [Copyright &y& Elsevier]