On compromise solutions in multiple objective programming
RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 2, pp. 383-390.

Compromise solutions, as feasible points as close as possible to the ideal (utopia) point, are important solutions in multiple objective programming. It is known in the literature that each compromise solution is a properly efficient solution if the sum of the image set and conical ordering cone is closed. In this paper, we prove the same result in a general setting without any assumption.

DOI : 10.1051/ro/2017071
Classification : 90C29
Mots-clés : Multiple objective programming, compromise solution, properly efficient solution
Soleimani–Damaneh, Majid 1 ; Zamani, Moslem 1

1 
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     author = {Soleimani{\textendash}Damaneh, Majid and Zamani, Moslem},
     title = {On compromise solutions in multiple objective programming},
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     publisher = {EDP-Sciences},
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Soleimani–Damaneh, Majid; Zamani, Moslem. On compromise solutions in multiple objective programming. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 2, pp. 383-390. doi : 10.1051/ro/2017071. http://www.numdam.org/articles/10.1051/ro/2017071/

[1] M. Ehrgott, Multicriteria Optimization. Springer, Berlin (2005) | MR | Zbl

[2] W.B. Gearhart, Compromise solutions and estimation of the noninferior set. J. Optim. Theory Appl. 28 (1979) 29–47 | DOI | MR | Zbl

[3] A. Geoffrion, Proper efficiency and the theory of vector maximization. J. Math. Anal. Appl. 22 (1968) 618–630 | DOI | MR | Zbl

[4] M. Henig, Proper efficiency with respect to cones. J. Optim. Theory Appl. 36 (1982) 387–407 | DOI | MR | Zbl

[5] K. Khaledian, E. Khorram and M. Soleimani–Damaneh, Strongly proper efficient solutions: efficient solutions with bounded trade-offs. J. Optim. Theory Appl. 168 (2016) 864–883 | DOI | MR | Zbl

[6] K. Khaledian and M. Soleimani–Damaneh, On efficient solutions with trade-offs bounded by given values. Numer. Functional Anal. Optimiz. 36 (2015) 1431–1447 | DOI | MR | Zbl

[7] Y. Sawaragi, H. Nakayama and T. Tanino, Theory of Multiobjective Optimization. Academic Press, Orlando, FL (1985) | MR | Zbl

[8] M. Soleimani-Damaneh, Nonsmooth optimization using Mordukhovich’s subdifferential. SIAM J. Control Optim. 48 (2010) 3403–3432 | DOI | MR | Zbl

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