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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
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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