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Characterisations of efficient sets in vector optimisation

Published online by Cambridge University Press:  17 April 2009

Nathalie Boissard
Nathalie Boissard
Affiliation:
Laboratoire d'Analyse non linéaire et OptimisationUniversité de Limoges123 avenue Albert Thomas 87060 Limoges CedexFrance e-mail: boissard@unilim.fr
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Abstract

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In this paper, we present characterisations of the sets of infima and efficient solutions and we give also a multiplier rule for these kinds of points. The results are established for a vector optimisation problem with C-convexlike criterion, C being a polyhedral cone.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 1 , February 1995 , pp. 43 - 54
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Dolecki, S. and Malivert, C., ‘General duality in vector optimization’, Optimization 27 (1993), 97–119.CrossRefGoogle Scholar
[2]Jahn, J., Mathematical vector optimization in partially ordered linear spaces (Peter Lang, Frankfurt, 1986).Google Scholar
[3]The Luc, Dinh, Theory of vector optimization, Lecture Notes in Economics and Mathematical Systems (Springer-Verlag, Berlin, Heidelberg, New York, 1989).CrossRefGoogle Scholar
[4]Postolica, V., ‘Vector optimization programs with multifunctions and duality’, Ann. Sci. Math. Québec 10 (1986), 85–102.Google Scholar
[5]Rockafellar, R.T., Convex analysis (Princeton University Press, Princeton, 1972).Google Scholar
[6]Sararagi, Y., Nakayama, H. and Tanino, T., Theory of multiobjective optimization (Academic Press, Orlando, 1985).Google Scholar
[7]Wang, S. and Li, Z., ‘Scalarization and Lagrange duality in multiobjective optimization,’, Optimization 26 (1992), 315–324.CrossRefGoogle Scholar
[8]Zlobec, S., ‘Two characterizations of Pareto Minima in convex multicriteria optimization’, Aplikace Matematiky 29 (1984), 342–349.Google Scholar