Optimality conditions via scalarization for a new [epsilon]-efficiency concept in vector optimization problems

In this work, necessary and sufficient conditions for approximate solutions of vector optimization problems are obtained via scalarization, i.e., by considering approximate solutions of associated scalar optimization problems. These conditions are proved through a new [epsilon]-efficiency concept and two very general assumptions on the scalarization that extend the usual order representing and monotonicity properties. Moreover, neither solidness hypothesis on the order cone nor monotonicity property on the scalarization are assumed.