Mixed E-duality for E-differentiable Vector Optimization Problems Under (Generalized) V-E-invexity

In this paper, a class of E-differentiable vector optimization problems with both inequality and equality constraints is considered. The so-called vector mixed E-dual problem is defined for the considered E-differentiable vector optimization problem with both inequality and equality constraints. Then, several mixed E-duality theorems are established under (generalized) V-E-invexity hypotheses.

On the Generic Uniqueness of Pareto-Efficient Solutions of Vector Optimization Problems

In this paper, the generic uniqueness of Pareto weakly efficient solutions, especially Pareto-efficient solutions, of vector optimization problems is studied by using the nonlinear and linear scalarization methods, and some further results on the generic uniqueness are proved. These results present that, for most of the vector optimization problems in the sense of the Baire category, the Pareto weakly efficient solution, especially the Pareto-efficient solution, is unique. Furthermore, based on these results, the generic Tykhonov well-posedness of vector optimization problems is given.