A new approach for solving non-linear non-smooth programming problems Ali Vahidian Kamyad School of mathematics, Ferdowsi University of Mashhad, Mashhad, Iran In this paper, we introduce a new approach to solve nonlinear programming problems also when the objective function (functions) or constraint function (functions) are non-smooth ones In this approach the nonlinear functions of the original problem is approximated by a piecewise linear functions. Then we find the global extremum of this approximated problem by solving a linear programming problem. Also, we will prove convergence of our approach One of the main advantages of our approach is that the approach may be extended for problems where objective function or constraint functions or both are non-smooth functions by introducing a novel definition of global weak differentiation in the sense of space . Also, other advantage of our approach is that we may obtain approximate solution by solving a corresponding a linear programming problem. Finally, numerical example are given to show the efficiency of the proposed approach to solve constraints nonlinear programming problems, especially when the objective function and constraint functions are non-smooth function.

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