Generalized Well-Posedness and Stability of Solutions in Set Optimization
Received:February 24, 2022  Revised:May 08, 2022
Key Words: well-posedness   stability   set optimization   Gerstewitz's function   upper semi-continuity   lower semi-continuity  
Fund Project:Supported by the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No.KYCX20_1321).
Author NameAffiliation
Congjun ZHANG School of Applied Mathematics, Nanjing University of Finance and Economics, Jiangsu 210023, P. R. China 
Zhiwei WANG School of Applied Mathematics, Nanjing University of Finance and Economics, Jiangsu 210023, P. R. China 
Sai LI Department of Mathematics, Nanjing University, Jiangsu 210093, P. R. China 
Hits: 318
Download times: 250
Abstract:
      The aim of this paper is to investigate the well-posedness and stability in set optimization. The notion of generalized well-posedness for set optimization problems is introduced using the embedding technique for the first time. Some criteria and characterizations of this type of well-posedness are derived. Sufficient conditions are also given for this type of well-posedness. Moreover, by virtue of a generalized Gerstewitz's function, the equivalent relation between this type of well-posedness and the generalized well-posedness of a scalar optimization problem is established. Finally, the upper semi-continuity and lower semi-continuity of weak efficient solution mappings for parametric set optimization problems are investigated under some suitable conditions.
Citation:
DOI:10.3770/j.issn:2095-2651.2022.06.008
View Full Text  View/Add Comment