Saddle point criteria for second order $\eta$-approximated vector optimization problems

Jayswal, Anurag, Jha, Shalini, and Choudhury, Sarita. "Saddle point criteria for second order $\eta $-approximated vector optimization problems." Kybernetika 52.3 (2016): 359-378. <http://eudml.org/doc/281543>.

@article{Jayswal2016,
abstract = {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.},
author = {Jayswal, Anurag, Jha, Shalini, Choudhury, Sarita},
journal = {Kybernetika},
keywords = {efficient solution; second order $\eta $-approximation; saddle point criteria; optimality condition; exact minimax penalty function; vector optimization problem; convex function; locally Lipschitz function},
language = {eng},
number = {3},
pages = {359-378},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Saddle point criteria for second order $\eta $-approximated vector optimization problems},
url = {http://eudml.org/doc/281543},
volume = {52},
year = {2016},
}

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
PB - Institute of Information Theory and Automation AS CR
VL - 52
IS - 3
SP - 359
EP - 378
AB - 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.
LA - eng
KW - efficient solution; second order $\eta $-approximation; saddle point criteria; optimality condition; exact minimax penalty function; vector optimization problem; convex function; locally Lipschitz function
UR - http://eudml.org/doc/281543
ER -