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

Antczak, 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 -