| In vector optimization theory there are several kind of approximate (efficient or Pareto) solutions. In the literature the most used is Loridan-Kutateladze approximate solution. However, we will show that there are examples of sequences of Loridan-Kutateladze approximate solutions such that the error vector tends to 0, but the distance between the solutions and the efficient set goes to infinity. This bad asymptotical behavior (metrically inconsistency) cannot happen with the approximate solutions in the sense of Tanaka or those in the sense of Bonnel. Some connections between these three different approximate solutions with respect to their asymptotical behavior will be presented. Moreover, different conditions ensuring a good asymptotical behavior (metrically consistency) of Loridan-Kutateladze sequences will be given. |
|
