A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations - Hamid Reza Erfanian; M. H. Noori Skandari; A. V. Kamyad (Journal of Mathematics)
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.