A Unified Approach for Scalar and Vector Optimization

  • Paolo Serafini
Part of the International Centre for Mechanical Sciences book series (CISM, volume 289)


This paper deals with some concepts related to the theory of convex programming. A theoretical framework is developed where both scalar and vector optimization can be accomodated. So far vector optimization the adopted point of view is much in the spirit of scalarization ; in this sense it is closely related to the papers by Pascoletti and Serafini1 and Jahn2,3. Moreover it develops in a more general way ideas first appeared in Serafini4.


Saddle Point Multi Objective Optimization Convex Cone Vector Optimization Vector Optimization Problem 
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  1. 1.
    Pascoletti, A. and Serafini, P., Scalarizing vector optimization problems, Journal of Optimization Theory and Applications, 42, 499, 1984.CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Jahn, J., Scalarization in vector optimization, Mathematical Programming, 29, 203, 1984.CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Jahn, J., Scalarization in multi objective optimization, this volume.Google Scholar
  4. 4.
    Serafini, P., Dual relaxation and branch-and-bound techniques for multi objective optimization, in Interactive decision analysis, Grauer, M., Wierzbicki, A., Eds., Springer, Berlin, 1984.Google Scholar
  5. 5.
    Rockafellar, R.T., Convex analysis, Princeton University Press, 1972.Google Scholar
  6. 6.
    Luenberger, D.G., Optimization by vector space methods, Wiley, New York, 1969.MATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 1985

Authors and Affiliations

  • Paolo Serafini
    • 1
  1. 1.Dipartimento di Matematica ed InformaticaUniversità di UdineItaly

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