集优化问题的广义适定性与解的稳定性

Generalized Well-Posedness and Stability of Solutions in Set Optimization

中文关键词:  适定性  稳定性  集优化  Gerstewitz函数  上半连续性  下半连续性

英文关键词:well-posedness  stability  set optimization  Gerstewitz's function  upper semi-continuity  lower semi-continuity

中文摘要:

      本文研究了集优化问题的适定性与解的稳定性. 首次利用嵌入技术引入了集优化问题的广义适定性概念, 得到了此类适定性的一些判定准则和特征, 并给出其充分条件. 此外, 借助一类广义Gerstewitz 函数, 建立了此类适定性与一类标量优化问题广义适定性之间的等价关系. 最后, 在适当条件下研究了含参集优化问题弱有效解映射的上半连续性和下半连续性.

英文摘要:

      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.