A SURVEY ON PARETO EFFICIENCY IN INFINITE DIMENSIONAL VECTOR SPACES

摘要

This research work was exhibited at MCDA'65, 12-14 April 2007, Poznan, Poland and it represents a survey on some recent studies concerning Pareto type efficiency in infinite dimensional ordered vector spaces. We present the main directions of research on the efficiency: the existence of the efficient points, the immediate properties and applications, our recent extension for the concept of the efficiency in infinite dimensional ordered vector spaces, emphasized by the approximate efficiency - a natural generalization of the efficiency and some important connections with other significant fields of research in Mathematics. New links between the approximate efficiency and the strong optimization by the full nuclear cones and our recent coincidence result between the approximate efficient points sets and the corresponding Choquet boundaries are specified. Several pertinent references conclude the study.