On variational principles, level sets, well-posedness, and epsilon-solutions in vector optimization

Using the concept for epsilon-efficient solutions introduced in Refs. 1 and 2, we extend the Ekeland variational principle and another variational principle given in Ref. 3 to vector-valued objective functions. This enables us to establish a kind of well-posedness for the resulting perturbed vector optimization problems. Based on this definition of epsilon-efficiency, we also formulate a concept for level sets and prove some results about the Kuratowski limits of level sets.