ABSTRACT
We often come across different kinds of real-world problems that can be written in the form of an optimization problem where the objective function is not necessarily differentiable in the classical sense. Therefore, several kinds of derivatives have been introduced and studied in the literature. In this chapter, we study some of these derivatives, namely, directional derivatives, Gaˆteaux derivatives, Dini derivatives, Dini-Hadamard derivatives, and Clarke derivatives. We present some fundamental properties of these derivatives. The mean value theorem, which is one of the most important results from calculus, has also been presented in terms of different kinds of derivatives.
