Generalized gradients of monotone type Original Research Article

We examine the properties of the subdifferential in the sense of Clarke of certain locally Lipschitz, quasi-convex functions. We prove that, even if they may not possess a pseudomonotone-type subdifferential, if we consider the operator A+∂f, where A is an operator of type (S)+, then the sum is pseudomonotone. A new type of subdifferential for Lipschitz functions is also presented. We prove some calculus rules and we establish that in the context of reflexive Banach spaces is an operator of type (M).