Saddle point criteria for second order $\eta $-approximated vector optimization problems
Kybernetika, Tome 52 (2016) no. 3, pp. 359-378
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library
The purpose of this paper is to apply second order $\eta$-approximation method introduced to optimization theory by Antczak [2] to obtain a new second order $\eta$-saddle point criteria for vector optimization problems involving second order invex functions. Therefore, a second order $\eta$-saddle point and the second order $\eta$-Lagrange function are defined for the second order $\eta$-approximated vector optimization problem constructed in this approach. Then, the equivalence between an (weak) efficient solution of the considered vector optimization problem and a second order $\eta$-saddle point of the second order $\eta$-Lagrangian in the associated second order $\eta$-approximated vector optimization problem is established under the assumption of second order invexity.
The purpose of this paper is to apply second order $\eta$-approximation method introduced to optimization theory by Antczak [2] to obtain a new second order $\eta$-saddle point criteria for vector optimization problems involving second order invex functions. Therefore, a second order $\eta$-saddle point and the second order $\eta$-Lagrange function are defined for the second order $\eta$-approximated vector optimization problem constructed in this approach. Then, the equivalence between an (weak) efficient solution of the considered vector optimization problem and a second order $\eta$-saddle point of the second order $\eta$-Lagrangian in the associated second order $\eta$-approximated vector optimization problem is established under the assumption of second order invexity.
DOI :
10.14736/kyb-2016-3-0359
Classification :
90C26, 90C29, 90C30, 90C46
Keywords: efficient solution; second order $\eta $-approximation; saddle point criteria; optimality condition
Keywords: efficient solution; second order $\eta $-approximation; saddle point criteria; optimality condition
@article{10_14736_kyb_2016_3_0359,
author = {Jayswal, Anurag and Jha, Shalini and Choudhury, Sarita},
title = {Saddle point criteria for second order $\eta $-approximated vector optimization problems},
journal = {Kybernetika},
pages = {359--378},
year = {2016},
volume = {52},
number = {3},
doi = {10.14736/kyb-2016-3-0359},
mrnumber = {3532512},
zbl = {06644300},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-3-0359/}
}
TY - JOUR AU - Jayswal, Anurag AU - Jha, Shalini AU - Choudhury, Sarita TI - Saddle point criteria for second order $\eta $-approximated vector optimization problems JO - Kybernetika PY - 2016 SP - 359 EP - 378 VL - 52 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-3-0359/ DO - 10.14736/kyb-2016-3-0359 LA - en ID - 10_14736_kyb_2016_3_0359 ER -
%0 Journal Article %A Jayswal, Anurag %A Jha, Shalini %A Choudhury, Sarita %T Saddle point criteria for second order $\eta $-approximated vector optimization problems %J Kybernetika %D 2016 %P 359-378 %V 52 %N 3 %U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-3-0359/ %R 10.14736/kyb-2016-3-0359 %G en %F 10_14736_kyb_2016_3_0359
Jayswal, Anurag; Jha, Shalini; Choudhury, Sarita. Saddle point criteria for second order $\eta $-approximated vector optimization problems. Kybernetika, Tome 52 (2016) no. 3, pp. 359-378. doi: 10.14736/kyb-2016-3-0359
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