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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

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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 
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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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