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Vector Optimization: Theory, Methods, and Application to Design Problems in Engineering

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Modern Methods of Optimization

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 378))

Abstract

This paper gives a short overview on important subjects of vector optimization and it examines present research directions in this area of optimization. In the theory we turn our attention to scalarization, optimality conditions and duality. Concerning the numerical methods we study only the class of interactive methods, a modified method of Polak and a method of reference point approximation. Finally, applications to problems of the design of a sandwich beam and a fluidized reactor-heater system are discussed.

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References

  1. M. Bleß, Sensitivität in der Vektoroptimierung (dissertation, University of Göttingen, 1990 ).

    Google Scholar 

  2. B. Brosowski and A. Conci, “On the Optimal Design of Stiffened Plates”, Proceedings COBEM 8.9 (1983), p. 169–178.

    Google Scholar 

  3. A. Charnes and W. Cooper, Management models and industrial applications of linear programming, Vol. 1 (Wiley, New York, 1961 ).

    Google Scholar 

  4. W. Dinkelbach, “Über einen Lösungsansatz zum Vektormaximumproblem”, in: M. Beckmann (ed.), Unternehmensforschung Heute ( Springer, Berlin 1971 ), p. 1–13.

    Chapter  Google Scholar 

  5. F. Y. Edgeworth, Mathematical Psychics ( Kegan Paul, London, 1881 ).

    Google Scholar 

  6. H. Eschenauer, J. Koski and A. Osyczka (eds.) Multicriteria Design Optimization ( Springer, Berlin, 1990 ).

    Google Scholar 

  7. H. Eschenauer and E. Schäfer, “Sandwichbalken mit Fachwerkunterbau” (manuscript, University of Siegen, 1989 ).

    Google Scholar 

  8. J. Jahn, Mathematical Vector Optimization in Partially Ordered Linear Spaces (P. Lang, Frankfurt, 1986 ).

    Google Scholar 

  9. J. Jahn, “Parametric Approximation Problems Arising in Vector Optimization”, JOTA 54 (1987) 503–516.

    Article  Google Scholar 

  10. J. Jahn and A. Merkel, “A Method of Reference Point Approximation for the Solution of Bicriterial Nonlinear Optimization Problems”, JOTA (to appear).

    Google Scholar 

  11. A. Kirsch, tV. Warth and J. Werner, Notwendige Optimalitätsbedingungen und ihre Anwendung ( Springer, Berlin, 1978 ).

    Book  Google Scholar 

  12. H. Kitagawa, N. Watanabe, Y. Nishimura and M. Matsubara, “Some Pathological Configurations of Noninferior Set Appearing in Multicriteria Optimization Problems of Chemical Processes”, JOTA. 98 (1982) 541–563.

    Article  Google Scholar 

  13. J. Klose, “Sensitivity Analysis Using the Tangent Derivative” (manuscript, University of Erlangen-Nürnberg, 1990 ).

    Google Scholar 

  14. J. Klose, “On the Numerical Solution of a Bicriterial Optimization Problem from Chemical Engineering” (manuscript, University of Erlangen-Nürnberg, 1990 ).

    Google Scholar 

  15. T. C. Koopmans, “Analysis of Production as an Efficient Combination of Activities”, in: T. C. Koopmans (ed.), Activity Analysis of Production and Allocation ( Wiley, New York, 1951 ), p. 33–97.

    Google Scholar 

  16. H. W. Kuhn and A. W. Tucker, “Nonlinear Programming”, in: J. Neyman, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (Berkeley, 1951 ), p. 481–492.

    Google Scholar 

  17. D. T. Luc and J. Jahn, “Axiomatic Approach to Duality in Optimization” (manuscript, University of Erlangen-Nürnberg, 1990 ).

    Google Scholar 

  18. V. Pareto, Cours d’Economie Politique (F. Rouge, Lausanne, 1896 ).

    Google Scholar 

  19. M. Petschke, Extremalstrahlen konvexer Kegel und komplementäre Ungleichungen (dissertation, Technical University of Darmstadt, 1989 ).

    Google Scholar 

  20. E. Polak, “On the Approximation of Solutions to Multiple Criteria Decision Making Problems”, in M. Zeleny (ed.), Multiple Criteria Decision Making, Kyoto 197.5 ( Springer, Berlin, 1976 ), p. 271–281.

    Chapter  Google Scholar 

  21. W. Stadler, “Initiators of Multicriteria Optimization”, in: J. Jahn und W. Krabs (eds.), Recent Advances and Historical Development of Vector Optimization ( Springer, Berlin, 1987 ), p. 3–47.

    Chapter  Google Scholar 

  22. T. Staib, Notwendige Optimalitätsbedingungen in der mehrkriteriellen Optimierung mit Anwendung auf Steuerungsprobleme (dissertation, University of Erlangen—Nürnberg, 1989 ).

    Google Scholar 

  23. P. Weidner, Ein Trennungskonzept und seine Anwendung auf Vektoroptimierungsverfahren (habilitation thesis, University of Halle, 1990 ).

    Google Scholar 

  24. D. Zhuang, Regularity and maximality properties of set-valued structures in optimization (dissertation, Dalhousie University, Halifax, 1989 ).

    Google Scholar 

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© 1992 Springer-Verlag Berlin Heidelberg

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Jahn, J. (1992). Vector Optimization: Theory, Methods, and Application to Design Problems in Engineering. In: Krabs, W., Zowe, J. (eds) Modern Methods of Optimization. Lecture Notes in Economics and Mathematical Systems, vol 378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02851-3_5

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  • DOI: https://doi.org/10.1007/978-3-662-02851-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55139-3

  • Online ISBN: 978-3-662-02851-3

  • eBook Packages: Springer Book Archive

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