Positivity ( IF 1 ) Pub Date : 2021-01-19 , DOI: 10.1007/s11117-020-00807-0 Chuang-liang Zhang , Nan-jing Huang
This paper is about the well-posedness and stability in set optimization with applications to vector-valued games involving uncertainty. Some characterizations for several types of well-posedness with their relations in set optimization are given under mild conditions. Some sufficient and necessary conditions for these types of well-posedness in set optimization are also given by using the local C-Lipschitz continuity. Moreover, the upper semi-continuity, lower semi-continuity and compactness of minimal solution mappings are studied for parametric set optimization involving the cone Lipschitz continuous set-valued mapping. Finally, some obtained results are applied to derive the well-posedness for vector-valued games with uncertainty.
中文翻译:
应用程序集优化中的适定性和稳定性
本文是关于集合优化中的适定性和稳定性,并将其应用于涉及不确定性的向量值游戏。在温和条件下给出了几种类型的适定性及其在集合优化中的关系的一些特征。通过使用局部C -Lipschitz连续性,还为集合优化中的这类适定性提供了一些充分必要的条件。此外,研究了最小解映射的上半连续性,下半连续性和紧致性,以进行涉及锥Lipschitz连续集值映射的参数集优化。最后,将获得的一些结果用于推导具有不确定性的向量值游戏的适定性。