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.

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In this paper, we investigate the problem of combating terrorism by the government, which is one of the most serious problems that direct governments and countries. We formulate the problem and use the Nash approach of a differential game to obtain the optimal strategies for combating terrorism. We study the relationship between each of the government’ strategies and terrorism when the government is on the defensive (reactive), and we study when the government expects terrorist attacks and develops its strategies to combat terrorism. Also, we study the relationship between government activity and its strategies as well as government activity and the strategy of terrorist organizations.