Generalized Monotone Nonsmooth Maps

Recent characterizations of various types of differentiable generalized monotone maps by Karamardian–Schaible–Crouzeix and their strengthened versions by Crouzeix–Ferland are extended to the nonsmooth case. For nondifferentiable locally Lipschitz maps necessary and/or sufficient conditions for quasimonotonicity, pseudomonotonicity and strict/ strong pseudomonotonicity are derived. To accomplish this, the generalized Jacobian in the sense of Clarke is employed.