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A notion of pseudo-differential on Riemannian manifolds is considered and a subdifferential calculus related to this subdifferential is presented and then by definition of pseudo-Hessian, a version of Taylor's expansion theorem is obtained. Moreover, characterizations of generalized convexity of continuous functions are obtained in terms of the generalized monotonicity of pseudo-differentials. [ABSTRACT FROM AUTHOR]

We study some classes of generalized convex functions, using a generalized differential approach. By this we mean a set-valued mapping which stands either for a derivative, a subdifferential or a pseudo-differential in the sense of Jeyakumar and Luc. Such a general framework allows us to avoid technical assumptions related to specific constructions. We establish some links between the corresponding classes of pseudoconvex, quasiconvex and another class of generalized convex functions we introduced. We devise some optimality conditions for constrained optimization problems. In particular, we get Lagrange–Kuhn–Tucker multipliers for mathematical programming problems. [ABSTRACT FROM PUBLISHER]