Unboundedness in Kasimbeyli’s scalarization

Kasimbeyli’s scalarization or conic scalarization is a useful tool for scalarizing which introduce by Kasimbeyli [5, 6]. This scalarization is proposed for determining all properly efficient elements in nonconvex vector optimization problem. In this paper, we show that if the Kasimbeyli s optimization problem is unbounded in below then the set of properly efficient points is empty.

Keywords:

Bishop-Phelps cone , Conic scalarization , Conic separation theorem , Proper efficiency