What does this research mean for the field?

The newly introduced concept of coderivatives at infinity for set-valued mappings provides complete characterizations of well-posedness, Mordukhovich’s criterion, and optimality conditions at infinity, yielding new insights even for classical smooth single-valued mappings. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The paper aims to establish the theory of coderivatives at infinity for set-valued mappings and their implications in optimization.

May 30, 2026

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

Key Points

The paper aims to establish the theory of coderivatives at infinity for set-valued mappings and their implications in optimization.
Introduced the concept of coderivatives at infinity for set-valued mappings.
Established well-posedness properties and Mordukhovich's criterion at infinity.
Provided optimality conditions specifically for set-valued optimization.
Established complete characterizations of well-posedness and optimality at infinity.
Results enhance understanding of classical smooth single-valued mappings.
Demonstrated new insights in the context of set-valued mappings optimization.

Abstract

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.

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