Extended and strongly extended well-posedness of set-valued optimization problems

X. X. Huang

Mathematical Methods of Operations Research, 2001, vol. 53, issue 1, 116 pages

Abstract: In this paper, we deal with the extended well-posedness and strongly extended well-posedness of set-valued optimization problems. These two concepts are generalizations of the extended well-posedness of real-valued optimization probems defined by Zolezzi. We obtain some criteria and characterizations of these two types of extended well-posedness, further generalizing most results obtained by Zolezzi for the extended well-posedness of scalar optimization problems. In the mean time, many results obtained by us for the extended well-posedness of vector optimization problems have been generalized to set-valued optimization. Finally, we present an approximate variational principle for set-valued maps, derive a necessary approximate optimality condition for set-valued optimization, based on which we introduce a condition, which is somewhat analogous to the Palais-Smale condition (C), and provide sufficient conditions for the extended and strongly extended well-posedness of set-valued optimization problems. Copyright Springer-Verlag Berlin Heidelberg 2001

Keywords: Key words: Set-valued optimization; asymptotically minimizing sequence; well-posedness; set-valued variational principle; stability (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (18)

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DOI: 10.1007/s001860000100

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