Subdifferential Calculus for Ordered Set-Valued Mappings between Infinite-Dimensional Spaces

TL;DR

This paper develops a subdifferential calculus framework for set-valued mappings in ordered infinite-dimensional spaces, with applications to vector and set optimization problems involving complex constraints.

Contribution

It introduces new sum and chain rules for subdifferentials of ordered set-valued mappings in infinite-dimensional spaces, expanding the theoretical foundation.

Findings

Established new sum rules for subdifferentials.

Derived chain rules under qualification conditions.

Applicable to vector and set optimization problems.

Abstract

The paper is devoted to developing subdifferential theory for set-valued mappings taking values in ordered infinite-dimensional spaces. This study is motivated by applications to problems of vector and set optimization with various constraints in infinite dimensions. The main results establish new sum and chain rules for major subdifferential constructions associated with ordered set-valued mappings under appropriate qualification and sequentially normal compactness conditions.