# Article

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Keywords:
second order $\eta$-approximated optimization problem; second order $\eta$-saddle point; second order $\eta$-Lagrange function; second order invex function with respect to $\eta$; second order optimality conditions
Summary:
In this paper, by using the second order $\eta$-approximation method introduced by Antczak [3], new saddle point results are obtained for a nonlinear mathematical programming problem involving second order invex functions with respect to the same function $\eta$. Moreover, a second order $\eta$-saddle point and a second order $\eta$-Lagrange function are defined for the so-called second order $\eta$-approximated optimization problem constructed in this method. Then, the equivalence between an optimal solution in the original mathematical programming problem and a second order $\eta$-saddle point of the second order $\eta$
References:
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