On Clarke's Subdifferential of Marginal Functions

TL;DR

This paper provides a new upper estimate for Clarke's subdifferential of marginal functions in Banach spaces, extending previous results by removing the need for the Asplund assumption.

Contribution

It introduces a general approach to estimate Clarke's subdifferential in Banach spaces without relying on the Asplund property.

Findings

Upper estimate of Clarke's subdifferential derived

Results applicable to general Banach spaces

Avoids Asplund assumption in derivations

Abstract

In this short note, we derive an upper estimate of Clarke's subdifferential of marginal functions in Banach spaces. The structure of the upper estimate is very similar to other results already obtained in the literature. The novelty lies on the fact that we derive our assertions in general Banach spaces, and avoid the use of the Asplund assumption.