Approximate necessary conditions for locally weak Pareto optimality |
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Authors: | L Gajek D Zagrodny |
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Institution: | (1) Mathematical Institute, PAN, Warsaw, Poland;(2) Technical University of ód , ód , Poland;(3) Institute of Mathematics, Technical University of ód , ód , Poland |
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Abstract: | Necessary conditions for a given pointx
0 to be a locally weak solution to the Pareto minimization problem of a vector-valued functionF=(f
1,...,f
m
),F:X R
m,X R
m, are presented. As noted in Ref. 1, the classical necessary condition-conv {Df
1(x
0)|i=1,...,m} T
*(X, x
0)![ne](/content/b251q268ugu25748/xxlarge8800.gif) 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.The authors would like to thank the anonymous referee for the suggestions which led to an improved presentation of the paper. |
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Keywords: | Multiobjective optimization Pareto optimality necessary conditions contingen cones |
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