Improperly Efficient Solutions in a Class of Vector Optimization Problems

TL;DR

This paper investigates improperly efficient solutions in linear fractional vector optimization problems, providing conditions that identify when all solutions are improperly efficient and offering new insights into proper efficiency.

Contribution

It introduces new sufficient and necessary conditions for improper and proper efficiency in linear fractional vector optimization with unbounded constraints.

Findings

All efficient solutions are improperly efficient under certain conditions.

New necessary conditions for improper efficiency are established.

Enhanced understanding of proper efficiency in linear fractional vector optimization.

Abstract

Improperly efficient solutions in the sense of Geoffrion in linear fractional vector optimization problems with unbounded constraint sets are studied 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.