# Abstract:

The purpose of this paper is to apply second order $\eta$-approximation method introduced to optimization theory by Antczak \cite{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.

# Keywords:

efficient solution, second order $\eta$-approximation, saddle point criteria, optimality condition

# Classification:

90C26, 90C29, 90C30, 90C46

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