Approximate necessary conditions for locally weak Pareto optimality

  • L. Gajek
  • D. Zagrodny
Contributed Papers


Necessary conditions for a given pointx0 to be a locally weak solution to the Pareto minimization problem of a vector-valued functionF=(f1,...,f m ),F:XRm,XRm, are presented. As noted in Ref. 1, the classical necessary condition-conv {Df1(x0)|i=1,...,m}∩T*(X, x0)≠⊘ need not hold when the contingent coneT is used. We have proven, however, that a properly adjusted approximate version of this classical condition always holds. Strangely enough, the approximation form>2 must be weaker than form=2.

Key Words

Multiobjective optimization Pareto optimality necessary conditions contingen cones 


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Copyright information

© Penum Publishing Corporation 1994

Authors and Affiliations

  • L. Gajek
    • 1
    • 2
  • D. Zagrodny
    • 3
  1. 1.Mathematical InstitutePANWarsawPoland
  2. 2.Technical University of ŁódźŁódźPoland
  3. 3.Institute of MathematicsTechnical University of ŁódźŁódźPoland

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