Acta Mathematica Sinica, English Series

, Volume 26, Issue 11, pp 2031–2040 | Cite as

On relations of vector optimization results with C 1,1 data

Article
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Abstract

In this article we prove that some of the sufficient and necessary optimality conditions obtained by Ginchev, Guerraggio, Luc [Appl. Math., 51, 5–36 (2006)] generalize (strictly) those presented by Guerraggio, Luc [J. Optim. Theory Appl., 109, 615–629 (2001)]. While the former paper shows examples for which the conditions given there are effective but the ones from the latter paper fail, it does not prove that generally the conditions it proposes are stronger. In the present note we complete this comparison with the lacking proof.

Keywords

C1,1 function generalized second-order directional derivative Dini derivative weakly efficient minimizer isolated minimizer of second-order 

MR(2000) Subject Classification

49K10 49J52 49J50 90C29 90C30 
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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Hradec KrálovéHradec KrálovéCzech Republic
  2. 2.Department of Mathematical Analysis and Applications of Mathematics, Faculty of SciencePalacký UniversityOlomoucCzech Republic

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