Monotonicity of Löwner operators and its applications to symmetric cone complementarity problems

We prove necessary and sufficient conditions for locally Lipschitz Lowner operators to be monotone, strictly monotone and strongly monotone. Utilizing our characterization of the strict monotonicity of Lowner operators, we generalize Mangasarian class of Nonlinear Complementarity Problem (NCP)-functions to the setting of symmetric cone complementarity problem. This affirmatively answers a question of Tseng [Math Program 83:159–185, 1998].