Saddle point criteria for second order $\eta$-approximated vector optimization problems
Anurag Jayswal, Shalini Duggal Jha, Sarita Choudhury · Kybernetika · 2016
summary: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.