The stability and extended well-posedness of the solution sets for set optimization problems via the Painlevé–Kuratowski convergence

Yu Han (), Kai Zhang and Nan-jing Huang ()
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Yu Han: Jiangxi University of Finance and Economics
Kai Zhang: Jiangxi University of Finance and Economics
Nan-jing Huang: Sichuan University

Mathematical Methods of Operations Research, 2020, vol. 91, issue 1, No 10, 175-196

Abstract: Abstract In this paper, we obtain the Painlevé–Kuratowski upper convergence and the Painlevé–Kuratowski lower convergence of the approximate solution sets for set optimization problems with the continuity and convexity of objective mappings. Moreover, we discuss the extended well-posedness and the weak extended well-posedness for set optimization problems under some mild conditions. We also give some examples to illustrate our main results.

Keywords: Set optimization problem; Painlevé–Kuratowski convergence; Stability; Extended well-posedness; 49J40; 49K40; 90C31 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s00186-019-00695-5

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