Kybernetika 52 no. 3, 359-378, 2016

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

Anurag Jayswal, Shalini Jha and Sarita ChoudhuryDOI: 10.14736/kyb-2016-3-0359


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.


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


90C26, 90C29, 90C30, 90C46


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