Coderivatives at Infinity of Set-Valued Mappings with Applications to Optimization

In this paper, the concept of coderivatives at infinity of set-valued mappings is introduced. Well-posedness properties at infinity of set-valued mappings as well as Mordukhovich’s criterion at infinity are established. Optimality conditions at infinity in set-valued optimization are also provided. The obtained results, which give new information even in the classical cases of smooth single-valued mappings, provide complete characterizations of the properties under consideration in the setting at infinity of set-valued mappings.

Funding: D. S. Kim was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) [Grant RS-2025-19622979]. T.-S. Pham is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) [Grant 101.04-2023.06].