A New Approach for Generalized Partial Derivatives of Non-smooth Functions

In this paper, we define the functional optimization problems corresponding to multi-variable smooth functions, so that their optimal solutions are partial derivatives of these functions. These functional optimization problems are applied for multi-variables nonsmooth functions, so that by solving these problems we obtain generalized partial derivatives. For this purpose, linear programming problems corresponding to the functional optimization problems are obtained, so that their optimal solutions give the approximate generalized partial derivatives. In some illustrative examples, we show the efficiency of our approach by obtaining the generalized partial derivative of some smooth and nonsmooth functions, respectively. doi:10.14456/WJST.2014.58