Abstract:

With the help of Ben-Tal's generalized algebraic operations, a new kind of functions, termed (h,φ)-Lipschitz functions, is introduced. The relationship between it and Lipschitz function is discussed.Generalized directional derivative and generalized gradient are developed and their properties are obtained. As an application, the relationship between generalized directional derivative and contingent cone is presented.

Key words: (h,φ)-Lipschitz function, Generalized directional derivative, Generalized gradient