In this paper we introduce a new definition of an E-differentiable convex function, which transforms a non-differentiable function to a differentiable function under an operator E : R n → R n . By this definition, we can apply Kuhn-Tucker and Fritz-John conditions for obtaining the optimal solution of mathematical programming with a non-differentiable function.
In this work, we will study a class of the duality problem of E-convex programming. The weak and strong theorems for the duality problem of E-convex programming are given to show the relation between the solutions of the dual and primal problems, and also we will prove some properties of the duality problem of E-convex programming.
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