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Journal of Mathematics
Volume 2013 (2013), Article ID 750834, 10 pages
http://dx.doi.org/10.1155/2013/750834
Research Article

A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations

Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad 9177948953, Iran

Received 29 August 2012; Accepted 19 November 2012

Academic Editor: Ellina Grigorieva

Copyright © 2013 Hamid Reza Erfanian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a new approach for solving nonsmooth optimization problems and a system of nonsmooth equations which is based on generalized derivative. For this purpose, we introduce the first order of generalized Taylor expansion of nonsmooth functions and replace it with smooth functions. In other words, nonsmooth function is approximated by a piecewise linear function based on generalized derivative. In the next step, we solve smooth linear optimization problem whose optimal solution is an approximate solution of main problem. Then, we apply the results for solving system of nonsmooth equations. Finally, for efficiency of our approach some numerical examples have been presented.