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Scalarization method for Levitin–Polyak well-posedness of vectorial optimization problems

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  • Li Zhu
  • Fu-quan Xia

Abstract

In this paper, we develop a method of study of Levitin–Polyak well-posedness notions for vector valued optimization problems using a class of scalar optimization problems. We first introduce a non-linear scalarization function and consider its corresponding properties. We also introduce the Furi–Vignoli type measure and Dontchev–Zolezzi type measure to scalar optimization problems and vectorial optimization problems, respectively. Finally, we construct the equivalence relations between the Levitin–Polyak well-posedness of scalar optimization problems and the vectorial optimization problems. Copyright Springer-Verlag Berlin Heidelberg 2012

Suggested Citation

  • Li Zhu & Fu-quan Xia, 2012. "Scalarization method for Levitin–Polyak well-posedness of vectorial optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 361-375, December.
    • Handle: RePEc:spr:mathme:v:76:y:2012:i:3:p:361-375
    DOI: 10.1007/s00186-012-0410-9
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    References listed on IDEAS

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    1. M. Durea, 2007. "Scalarization for pointwise well-posed vectorial problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 409-418, December.
    2. E. Miglierina & E. Molho & M. Rocca, 2005. "Well-Posedness and Scalarization in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 126(2), pages 391-409, August.
    3. X. X. Huang, 2001. "Pointwise Well-Posedness of Perturbed Vector Optimization Problems in a Vector-Valued Variational Principle," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 671-684, March.
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    Cited by:

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