Monotonicity of L”{o}wner Operators and Its Applications to Symmetric Cone Complementarity Problems

This paper focuses on monotone L\"{o}wner operators in Euclidean Jordan algebras and their applications to the symmetric cone complementarity problem (SCCP). We prove necessary and sufficient conditions for locally Lipschitz L\"{o}wner operators to be monotone, strictly monotone and strongly monotone. We also study the relationship between monotonicity and operator-monotonicity of L\"{o}wner operators. As a by-product of our results, we establish a new class of C-functions for SCCP, which is an extension of the Mangasarian class of NCP-functions for the nonlinear complementarity problem, and present some characterizations of the C-functions for SCCP under certain assumptions.


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