# Outer limits of subdifferentials for min-max type functions

## TL;DR

This paper extends the outer subdifferential concept to min-max functions and clarifies the relationship between the outer subdifferential of a support function and the end set of its subdifferential, addressing open questions.

## Contribution

It generalizes the outer subdifferential for min-max functions and resolves an open problem about the connection between support functions and subdifferential end sets.

## Key findings

- Extended outer subdifferential to pointwise minima of Lipschitz functions
- Provided a relation between the outer subdifferential of support and subdifferential end set
- Addressed an open question in subdifferential theory

## Abstract

We generalise the outer subdifferential constructon suggested by C\'anovas, Henrion, L\'opez and Parra for max type functions to pointwise minima of regular Lipschitz functions. We also answer an open question about the relation between the outer subdifferential of the support of a regular function and the end set of its subdifferential posed by Li, Meng and Yang.