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.
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This work was supported by the National Natural Science Foundation of China (10671135), the Key Project of Chinese Ministry of Education (212147), the Doctoral Fund of Ministry of Education of China (20105134120002), Applied Research Project of Sichuan Province (2010JY0121).
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Zhu, L., Xia, Fq. Scalarization method for Levitin–Polyak well-posedness of vectorial optimization problems. Math Meth Oper Res 76, 361–375 (2012). https://doi.org/10.1007/s00186-012-0410-9
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DOI: https://doi.org/10.1007/s00186-012-0410-9