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.

中文翻译：

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一类向量优化问题中效率不高的解

本文首次系统地研究了具有无界约束集的线性分数向量优化问题中Geoffrion意义上的不适当有效解。我们给出两组条件，以确保给定问题的所有有效解决方案都是不正确的。我们还获得了有效解决方案不正确有效的必要条件。结果，我们为 Geoffrion 的适当效率提供了新的充分条件。获得的结果丰富了我们对线性分数向量优化中适当有效解决方案的知识。