Mathematical Methods of Operations Research

, Volume 51, Issue 3, pp 479–494 | Cite as

Steepest descent methods for multicriteria optimization

  • Jörg Fliege
  • Benar Fux Svaiter


We propose a steepest descent method for unconstrained multicriteria optimization and a “feasible descent direction” method for the constrained case. In the unconstrained case, the objective functions are assumed to be continuously differentiable. In the constrained case, objective and constraint functions are assumed to be Lipshitz-continuously differentiable and a constraint qualification is assumed. Under these conditions, it is shown that these methods converge to a point satisfying certain first-order necessary conditions for Pareto optimality. Both methods do not scalarize the original vector optimization problem. Neither ordering information nor weighting factors for the different objective functions are assumed to be known. In the single objective case, we retrieve the Steepest descent method and Zoutendijk's method of feasible directions, respectively.

Key words: Multicriteria optimization, multi-objective programming, vector optimization, Pareto points, steepest descent 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Jörg Fliege
    • 1
  • Benar Fux Svaiter
    • 2
  1. 1.Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany (e-mail:
  2. 2.Instituto de Matemática Pura e Aplicada, Jardim Botanico, Estrada Dona Castorina 110, Rio de Janeiro, RJ 22460-320, Brasil (e-mail:

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