Coderivatives at infinity of set-valued mappings

2023/11/30 by Do Sang Kim, Phạm Tiến Sơn, Kim, Do Sang +5 · 1 citation
Computer Science · Mathematics · #49J52 #49J53 #49K27 #49K40 #90C30 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2311.18370

openalex publication_date 2023/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. Fermat's rule at infinity in set-valued optimization is 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.

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• Directional Subdifferentials at Infinity and Its Applications

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