The borwein proper efficiency in linear fractional vector optimization

Borwein's properness of the efficient solutions of linear fractional vector optimization problems ( LFVOP s ) is studied for the first time in this paper. We show that: (i) The Borwein properly efficient solution set of a LFVOP can differ from the efficient solution set; (ii) For some LFVOPs , the Geoffrion properly efficient solution set can be a proper subset of the Borwein properly efficient solution set; (iii) For some nonconvex LFVOPs , the Borwein properly efficient solution set can coincide with the efficient solution set. Other major results of our paper are verifiable sufficient conditions for an efficient point of a LFVOP to be a Borwein's properly efficient point of the problem. For further investigations, some open questions are formulated. © 2019 Yokohama Publications. All rights reserved.