An axiomatic approach to approximate solutions in vector optimization
In vector optimization many notions of approximate solution have been proposed in the literature. In this paper an axiomatic approach is introduced in order to study the approximate solution map of a vector optimization problem in the image space. An impossibility result is proved in the sense that, whenever all of the axioms are satisfied, either the set of the approximate solutions is a subset of the exact solution of the problem (the weakly efficient frontier), or it coincides with the whole admissible set. Moreover, the geometry of the approximate solution map is studied in the special case of polyhedral ordering cones generated by a base of R. Finally, we study the shape of the approximate solution map under the assumption of weak approximation consistency.
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| Length: | 30 pages |
| Date of creation: | Sep 2005 |
| Handle: | RePEc:ins:quaeco:qf0507 |
| Contact details of provider: | Postal: Via Ravasi 2-21100 Varese Web page: http://www.uninsubria.it/uninsubria/facolta/econo.html More information through EDIRC
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References listed on IDEAS
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- Norde, Henk & Patrone, Fioravante & Tijs, Stef, 2000.
"Characterizing properties of approximate solutions for optimization problems,"
Mathematical Social Sciences,
Elsevier, vol. 40(3), pages 297-311, November.
- Norde, H.W. & Patrone, F. & Tijs, S.H., 1996. "Characterizing properties of approximate solutions for optimization problems," Discussion Paper 1996-101, Tilburg University, Center for Economic Research.
- Norde, H.W. & Patrone, F. & Tijs, S.H., 2000. "Characterizing properties of approximate solutions for optimization problems," Other publications TiSEM 11a62d7d-2aae-4602-b7c9-2, Tilburg University, School of Economics and Management.
- Graziano Pieri & Fioravante Patrone & Anna Torre & Stef Tijs, 1998. "On consistent solutions for strategic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 191-200.
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- Peleg, B. & Tijs, S., 1993. "The Consistency Principle for Games in Strategic Form," Papers 9306, Tilburg - Center for Economic Research.
- Peleg, B. & Tijs, S.H., 1996. "The consistency principle for games in strategic form," Other publications TiSEM fc27db2d-b84c-44ba-95a1-0, Tilburg University, School of Economics and Management.
- Peleg, B. & Tijs, S.H., 1993. "The consistency principle for games in strategic form," Discussion Paper 1993-6, Tilburg University, Center for Economic Research.
- Patrone, F. & Pieri, G. & Tijs, S.H. & Torre, A., 1998. "On consistent solutions for strategic games," Other publications TiSEM cc482511-a079-4067-88b2-0, Tilburg University, School of Economics and Management.
- Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
- repec:spr:compst:v:58:y:2003:i:3:p:375-385 is not listed on IDEAS
- E. Miglierina & E. Molho, 2003. "Well-posedness and convexity in vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(3), pages 375-385, December. Full references (including those not matched with items on IDEAS)
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