SOME APPLICATIONS OF NEAR (C, ε)-SUBCONVEXLIKENESS IN VECTOR OPTIMIZATION PROBLEMS WITH SET-VALUED MAPS

The main aim of this work is to study (C, epsilon)-Benson proper efficient elements of a vector optimization problem with nearly (C, epsilon)-subconvexlike set-valued maps. First, some properties of near (C, epsilon)-subconvexlikeness are discussed. Then, Lagrangian multiplier theorem for (C, epsilon)-Benson proper efficient elements of a constrained vector optimization problem with set-valued maps is obtained by using the technique of linear scalarization. Our results generalize and improve other similar results in the literature.