# Saddle points criteria via a second order $\eta $-approximation approach for nonlinear mathematical programming involving second order invex functions

Kybernetika (2011)

- Volume: 47, Issue: 2, page 222-240
- ISSN: 0023-5954

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topAntczak, Tadeusz. "Saddle points criteria via a second order $\eta $-approximation approach for nonlinear mathematical programming involving second order invex functions." Kybernetika 47.2 (2011): 222-240. <http://eudml.org/doc/196550>.

@article{Antczak2011,

abstract = {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 $},

author = {Antczak, Tadeusz},

journal = {Kybernetika},

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 optimality conditions; second order -approximated optimization problem; second order -saddle point; second order -Lagrange function; second order invex function with respect to },

language = {eng},

number = {2},

pages = {222-240},

publisher = {Institute of Information Theory and Automation AS CR},

title = {Saddle points criteria via a second order $\eta $-approximation approach for nonlinear mathematical programming involving second order invex functions},

url = {http://eudml.org/doc/196550},

volume = {47},

year = {2011},

}

TY - JOUR

AU - Antczak, Tadeusz

TI - Saddle points criteria via a second order $\eta $-approximation approach for nonlinear mathematical programming involving second order invex functions

JO - Kybernetika

PY - 2011

PB - Institute of Information Theory and Automation AS CR

VL - 47

IS - 2

SP - 222

EP - 240

AB - 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 $

LA - eng

KW - 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 optimality conditions; second order -approximated optimization problem; second order -saddle point; second order -Lagrange function; second order invex function with respect to

UR - http://eudml.org/doc/196550

ER -

## References

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