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On duality in the vectorial control-approximation problem

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Abstract

The author formulates vectorial dual problems for a certain class of vectorial control-approximation problems in real reflexive Banach spaces. A number of propositions concerning duality are derived. Corresponding propositions are mentioned for the special case of the vectorial location problems.

Zusammenfassung

In der Arbeit werden für eine Klasse von vektoriellen Steuer-Approximationsproblemen in reellen reflexiven Banachräumen vektorielle Dualprobleme konstruiert und Dualitätseigenschaften hergeleitet. Als Spezialfall ergeben sich entsprechende Aussagen für vektorielle Standortprobleme.

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References

  • Borwein JM (1977) Proper efficient points for maximation with respect to cones. SIAM J Control Optim 15:57–63

    Google Scholar 

  • Brumelle S (1981) Duality for multiple objective convex programs. Math of Operations Research 6:159–172

    Google Scholar 

  • Chalmet LG, Francis RL (1981) Finding efficient solutions for rectilinear distance location problems efficiently. European Journal of Operational Research 6:117–124

    Google Scholar 

  • Durier R (1987) Sets of efficiency in a normed space and inner product. In: Krabs W, Jahn J (eds) Lecture Notes in Economics and Mathematical Systems. Springer, Berlin Heidelberg New York 294:114–128

    Google Scholar 

  • Durier R, Michelot Ch (1986) Sets of efficient points in a normed space. J Math Appl 117:506–528

    Google Scholar 

  • Ekeland J, Temam R (1976) Convex analysis and variational problems. North-Holland, Amsterdam

    Google Scholar 

  • Goeffrion AM (1968) Proper efficiency and the theory of vector maximization. J Math Anal Appl 22:618–630

    Google Scholar 

  • Gerth Ch, Pöhler K (1988) Dualität und algorithmische Anwendung beim vektoriellen Standortproblem. Optimization 19:491–512

    Google Scholar 

  • Gerth Ch, Göpfert A, Pöhler K (1988) Vektorielles Standortproblem und Dualität. Wiss Z Karl-Marx-Universität, Leipzig. Math-Naturwiss R 37:305–312

    Google Scholar 

  • Jahn J (1986) Mathematical vector optimization in partially ordered linear spaces. Meth u Verf d math Phys 31. Verlag Peter Lang, Frankfurt

    Google Scholar 

  • Jahn J (1983) Zur vektoriellen linearen Tschebyscheff-Approximation. Math Operationsforsch u Statistik. Ser Optimization 14:577–591

    Google Scholar 

  • Juel H (1981) Bounds in the generalized Weber problem under locational uncertainty. Operations Research 29:1219–1227

    Google Scholar 

  • Kuhn H-W (1967) On a pair of dual nonlinear programs. In: Abadie J (ed) Nonlinear programming. Wiley, New York, pp 37–54

    Google Scholar 

  • Kuhn H-W (1973) A note on Fermat's problem. Math Progr 4:98–107

    Google Scholar 

  • Lai HC, Yang LS (1989) Strong duality for infinite dimensional vector valued programming problems. J Optim Theor Appl 62:449–466

    Google Scholar 

  • Loridan P (1984) A dual approach to the generalized Weber problem under locational uncertainty. Cahiers du CERO 26:241–253

    Google Scholar 

  • Rubinštein GŠ (1973) Issledovanija dvoistvennym ekstremal'nym zadačam. Optimizacija. Akademija Nauk Novosibirsk 9:13–149

    Google Scholar 

  • Wanka G (1989) Dualität beim skalaren und vektoriellen Standortproblem. Wiss Z TH Merseburg 31:682–687

    Google Scholar 

  • Wanka G (1990) Dualität beim skalaren Standortproblem (in preparation)

  • Wendell RE, Hurter AP, Lowe TJ (1977) Efficient points in location problems. AIIE Transactions 9:238–246

    Google Scholar 

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Wanka, G. On duality in the vectorial control-approximation problem. ZOR - Methods and Models of Operations Research 35, 309–320 (1991). https://doi.org/10.1007/BF01417520

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  • DOI: https://doi.org/10.1007/BF01417520

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