Abstract：In this note, we give an equivalent relationship between Geoffrion properly efficient solutions of the original and transformed mutliobjective optimization problems. This result is a slightly modified version of the work of Zarepisheh and Pardalos[Annals of Operations Research, 2017, 249(1-2):5-15]. Furthermore, we give an example to show the modified theorem.
Geoffrion A M. Proper efficiency and the theory of vector maximization. Journal of Mathematical Analysis and Applications, 1968, 22(3):618-630
[2]
Choo E U, Atkins D R. Proper efficiency in nonconvex multicriteria programming. Mathematics of Operations Research, 1983, 8(3):467-470
[3]
Bowman V J. On the relationship of the Tchebycheff norm and the efficient frontier of multiple-criteria objectives Multiple Criteria Decision Making. Berlin, Heidelberg:Springer, 1976:76-86
[4]
Antczak T. On G-invex multiobjective programming part I. Optimality. Journal of Global Optimization, 2009, 43(1):97-109
[5]
Sawaragi Y, Nakayama H, Tanino T. Theory of Multiobjective Optimization. New York:Academic Press, 1985
[6]
Zarepisheh M, Pardalos P M. An equivalent transformation of multi-objective optimization problems. Annals of Operations Research, 2017, 249(1-2):5-15
2020, Vol. 43 
