From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules

TL;DR

This paper develops precise calculus rules for directed subdifferentials, extending their applicability from quasidifferentiable to a broader class of directed subdifferentiable functions, and establishes related optimality conditions.

Contribution

It introduces exact calculus rules and optimality conditions for directed subdifferentials in a new class of functions, expanding the theoretical framework.

Findings

Derived exact calculus rules for directed subdifferentials.

Extended the theory from quasidifferentiable to directed subdifferentiable functions.

Established optimality conditions, chain rule, and mean-value theorem.

Abstract

We derive exact calculus rules for the directed subdifferential defined for the class of directed subdifferentiable functions. We also state optimality conditions, a chain rule and a mean-value theorem. Thus we extend the theory of the directed subdifferential from quasidifferentiable to directed subdifferentiable functions.