Rho-subdifferential and its applications to optimization problems

The notion of $ \rho $-quasiconvex functions is introduced and investigated. A characterization of a differentiable $ \rho $-quasiconvex function is presented as well. Furthermore, the notion of $ \rho $-subdifferential is introduced, and a sum formula for the $ \rho $-subdifferential of a sum of two $ \rho $-quasiconvex functions is established. As an application, some optimality conditions are given to $ \rho $-quasiconvex vector optimization problems by $ \rho $-subdifferentials.