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Improperly efficient solutions in a class of vector optimization problems

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Abstract

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.

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Acknowledgements

Nguyen Thi Thu Huong was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 06/2020/STS01. The authors would like to thank Vietnam Institute for Advanced Study in Mathematics (VIASM) for hospitality during our recent stay at the Institute. Careful readings and significant suggestions of the two anonymous referees are gratefully acknowledged.

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  1. Department of Mathematics, Faculty of Information Technology, Le Quy Don Technical University, 236 Hoang Quoc Viet, Hanoi, Vietnam

    Nguyen Thi Thu Huong

  2. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, 10307, Vietnam

    Nguyen Dong Yen

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  1. Nguyen Thi Thu Huong
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  2. Nguyen Dong Yen
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Correspondence to Nguyen Dong Yen.

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Huong, N.T.T., Yen, N.D. Improperly efficient solutions in a class of vector optimization problems. J Glob Optim 82, 375–387 (2022). https://doi.org/10.1007/s10898-021-01069-0

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