Geoffrion’s proper efficiency in linear fractional vector optimization with unbounded constraint sets

N. T. T. Huong (), J.-C. Yao () and N. D. Yen ()
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N. T. T. Huong: Le Quy Don Technical University
J.-C. Yao: China Medical University Hospital, China Medical University
N. D. Yen: Vietnam Academy of Science and Technology

Journal of Global Optimization, 2020, vol. 78, issue 3, No 6, 545-562

Abstract: Abstract Choo (Oper Res 32:216–220, 1984) has proved that any efficient solution of a linear fractional vector optimization problem with a bounded constraint set is properly efficient in the sense of Geoffrion. This paper studies Geoffrion’s properness of the efficient solutions of linear fractional vector optimization problems with unbounded constraint sets. By examples, we show that there exist linear fractional vector optimization problems with the efficient solution set being a proper subset of the unbounded constraint set, which have improperly efficient solutions. Then, we establish verifiable sufficient conditions for an efficient solution of a linear fractional vector optimization to be a Geoffrion properly efficient solution by using the recession cone of the constraint set. For bicriteria problems, it is enough to employ a system of two regularity conditions. If the number of criteria exceeds two, a third regularity condition must be added to the system. The obtained results complement the above-mentioned remarkable theorem of Choo and are analyzed through several interesting examples, including those given by Hoa et al. (J Ind Manag Optim 1:477–486, 2005).

Keywords: Linear fractional vector optimization; Efficient solution; Gain-to-loss ratio; Geoffrion’s properly efficient solution; Unbounded constraint set; Direction of recession; Regularity condition; 90C29; 90C32; 49K30; 49N60 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-020-00927-7

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