Improperly efficient solutions in a class of vector optimization problems

Improperly efficient solutions in the sense of Geoffrion in linear fractional vector optimization problems with unbounded constraint sets are studied systematically for the first time in this paper. We give two sets of conditions which assure that all the efficient solutions of a given problem are improperly efficient. We also obtain necessary conditions for an efficient solution to be improperly efficient. As a result, we have new sufficient conditions for Geoffrion’s proper efficiency. The obtained results enrich our knowledge on properly efficient solutions in linear fractional vector optimization. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.