Subdifferential calculus and ideal solutions for set optimization problems

TL;DR

This paper develops calculus rules for subdifferentials of set-valued maps and applies them to establish optimality conditions for a specific class of solutions in set optimization problems.

Contribution

It introduces new subdifferential calculus rules for set-valued maps and uses these to derive optimality conditions for ideal solutions in set optimization.

Findings

Derived basic calculus rules for subdifferentials of set-valued maps.

Established optimality conditions for a class of solutions in set optimization.

Enhanced understanding of subdifferential structures in set-valued analysis.

Abstract

We explore the possibility to derive basic calculus rules for some subdifferential constructions associated to set-valued maps between normed vector spaces. Then, we use these results in order to write optimality conditions for a special kind of solutions for set optimization problems.