On Variational Principles, Level Sets, Well-Posedness, and ε-Solutions in Vector Optimization

Using the concept for ε-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 ε-efficiency, we also formulate a concept for level sets and prove some results about the Kuratowski limits of level sets.