# Article

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Keywords:
mathematical programming; second order $\eta$-approximated optimization problem; second order invex function; second order optimality conditions
Summary:
A new approach for obtaining the second order sufficient conditions for nonlinear mathematical programming problems which makes use of second order derivative is presented. In the so-called second order $\eta$-approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order $\eta$-approximation of both the objective function and the constraint function constituting the original problem. The equivalence between the nonlinear original mathematical programming problem and its associated second order $\eta$-approximated optimization problem is established under second order invexity assumption imposed on the functions constituting the original optimization problem.
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