On weakly efficient solutions for semidefinite linear fractional vector optimization problems

We consider a scmidcfinite linear fractional vector optimization problem (FVP) and establish optimality theorems for weakly efficient solutions for (FVP), which hold without any constraint qualification. We first discuss the relation between weakly efficient solution of (FVP) and one of its related linear vector optimization problem (LVP). By using the relation and the maximum function of objetive functions of (FVP), we obtain our optimality theorems for weakly efficient solutions for (FVP), and then we give examples showing how to use our optimality theorems for finding weakly efficient solutions for (FVP). Moreover, we formulate vector dual problem (VD) for (FVP), which is a kind of vector version of Wolfe dual problem, and establish duality theorems for (FVP) and (VD), which hold without any constraint qualification.