Geodesic
Saddle points criteria via a second order $\eta $-approximation approach for nonlinear mathematical programming involving second order invex functions
Kybernetika, Tome 47 (2011) no. 2, pp. 222-240.

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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 $
Classification : 90C26, 90C46
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 
@article{KYB_2011__47_2_a3,
     author = {Antczak, Tadeusz},
     title = {Saddle points criteria via a second order $\eta $-approximation approach for nonlinear mathematical programming involving second order invex functions},
     journal = {Kybernetika},
     pages = {222--240},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2011},
     mrnumber = {2828574},
     zbl = {1242.90171},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2011__47_2_a3/}
}
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Antczak, Tadeusz. Saddle points criteria via a second order $\eta $-approximation approach for nonlinear mathematical programming involving second order invex functions. Kybernetika, Tome 47 (2011) no. 2, pp. 222-240. http://geodesic.mathdoc.fr/item/KYB_2011__47_2_a3/