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Finding Efficient Points in Multiobjective Quadratic Programming with Strictly Convex Objective Functions

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Book cover Advances in Multiple Objective and Goal Programming

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 455))

Abstract

In this work we consider the unconstrained multiobjective quadratic problem with strictly convex objective functions, (PCM — D). Firstly we expose a technique to determine the equations of the efficient points supposing that there are only two objective functions. This method is based on results on quadratic forms withdrawals by Gantmacher. Secondly, the technique explained is extended to calculate the equations of the efficient points of the general problem (PCM — D).

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References

  1. Beato-Moreno, A. Eficiencia en Programación Cuadrdtica Multiobjetivo. Ph. D. Thesis (Unpublished), 1995.

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  2. Chankong, V. and Haimes, Y. Y. Multiobjective Decision Making: Theory and Methodology. Elsevier Science Publishing Co. Inc., North-Holland, 1983.

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  3. Gantmacher, F.R. The Theory of Matrices. Vol I and II. Chelsea Publishing Company, New York, N.Y., 1959.

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  4. Ruiz-Canales, P.–Rufian Lizana, A. A Characterization of Weakly Efficient Points. Mathematical Programming. Vol 68 (1995), N. 2, pp. 205–212.

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  5. Warburton, A.R. Quasiconcave Vectir Maximization: Connectedness of the Set Pareto-Optimal and Weak Pareto-Optimal Alternatives. Journal of Optimization Theory and Applicattions. Vol. 40 (1983), PP. 537–557.

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Author information

Authors and Affiliations

  1. Departamento de Estadística e Investigación Operativa. Facultad de Matemáticas, Universidad de Sevilla, España

    A. Beato-Moreno, P. Luque-Calvo, R. Osuna-Gómez & A. Rufián-Lizana

Authors
  1. A. Beato-Moreno
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  2. P. Luque-Calvo
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  3. R. Osuna-Gómez
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  4. A. Rufián-Lizana
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Editor information

Editors and Affiliations

  1. Departamento de Economía Aplicada (Matemáticas) Facultad de Ciencias Económicas y Empresariales, University of Málaga, Campus El Ejido s/n, 29071, Málaga, Spain

    Rafael Caballero  & Francisco Ruiz  & 

  2. Faculty of Management Science, University of Georgia, 206 Brooks Hall, 30602-6255, Athens, Georgia, USA

    Ralph Steuer

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© 1997 Springer-Verlag Berlin Heidelberg

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Beato-Moreno, A., Luque-Calvo, P., Osuna-Gómez, R., Rufián-Lizana, A. (1997). Finding Efficient Points in Multiobjective Quadratic Programming with Strictly Convex Objective Functions. In: Caballero, R., Ruiz, F., Steuer, R. (eds) Advances in Multiple Objective and Goal Programming. Lecture Notes in Economics and Mathematical Systems, vol 455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46854-4_40

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  • DOI: https://doi.org/10.1007/978-3-642-46854-4_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63599-4

  • Online ISBN: 978-3-642-46854-4

  • eBook Packages: Springer Book Archive

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