Solvability based on E-property for the nonlinear symmetric cone complementarity problem

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, E 0 -property. And then we study the implications among these E-properties. In particular, the quad E-property is equivalent to the E-property. The K -copositive property implies the E 0 -property. The uniform Jordan E-property is proved to have the E 0 and R 0 -properties. Based on the E-properties, we get some sufficient conditions to guarantee the solution existence for the nonlinear symmetric cone complementarity problem.

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