Improperly efficient solutions in a class of vector optimization problems

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