Major
Mathematics
Anticipated Graduation Year
2026
Access Type
Open Access
Abstract
An existing form of approximating a non-differentiable function, f, is to slide a convex set, A, along the graph of f and take the lower boundary to form a differentiable function g. Our work reveals that sliding a convex set, A, under the graph of f gives the same approximation function, g, as sliding the set A-A along f. Additionally, sliding a convex set, A, under f is the same as sliding -A under f, or A-A along f. Due to this, if A is smooth from above or below, the approximation function g is essentially differentiable.
Faculty Mentors & Instructors
Dr Rafal Goebel
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Sliding a convex set under a convex function
An existing form of approximating a non-differentiable function, f, is to slide a convex set, A, along the graph of f and take the lower boundary to form a differentiable function g. Our work reveals that sliding a convex set, A, under the graph of f gives the same approximation function, g, as sliding the set A-A along f. Additionally, sliding a convex set, A, under f is the same as sliding -A under f, or A-A along f. Due to this, if A is smooth from above or below, the approximation function g is essentially differentiable.
Comments
Funded by the Rataj Fellowship