ε–Optimality to approximation in partially ordered spaces

Abstract

Approximation problems with vecior–valued norms are considered, where The solution concept is that of proper efficiency in multicriterial optimization. From that one a notion of approximately efficient solutions is derived, so called e–properly efficient solutions. Using Ekeland’s well known variational principle it results a slightly perturbed approximation Problem for which a dual problem and a strong duality assertion is established. That is used to get characterizing conditions for an appropriate approximate solution to the original problem. These conditions can be interpreted as generalized Kolmogorov–conditions refering to the well–known Kolmogorov–conditions in scalar best approximation.