A New Approach for the Generalized First Derivative and Extension It to the Generalized Second Derivative of Nonsmooth Functions

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Hamid Reza Erfanian 1,* M. H. Noori Skandari 1 A.V. Kamyad 1

1. Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

* Corresponding author.

DOI: https://doi.org/10.5815/ijisa.2013.04.10

Received: 11 Apr. 2012 / Revised: 9 Aug. 2012 / Accepted: 27 Oct. 2012 / Published: 8 Mar. 2013

Index Terms

Generalized Derivative, Smooth and Nonsmooth Functions, Linear Programming, Optimization


In this paper, first derivative of smooth function is defined by the optimal solution of a special optimization problem. In the next step, by using this optimization problem for nonsmooth function, we obtain an approximation for first derivative of nonsmooth function which it is called generalized first derivative. We then extend it to define generalized second derivative for nonsmooth function. Finally, we show the efficiency of our approach by evaluating derivative and generalized first and second derivative of some smooth and nonsmooth functions, respectively.

Cite This Paper

Hamid Reza Erfanian, M. H. Noori Skandari, A.V. Kamyad, "A New Approach for the Generalized First Derivative and Extension It to the Generalized Second Derivative of Nonsmooth Functions", International Journal of Intelligent Systems and Applications(IJISA), vol.5, no.4, pp.100-107, 2013. DOI:10.5815/ijisa.2013.04.10


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