# Optimization on fractal sets

## TL;DR

This paper investigates the conditions for the existence of extrema of functions on self-similar fractal sets and introduces a discrete gradient algorithm to locate these extrema.

## Contribution

It provides necessary and sufficient conditions for extrema on fractals and proposes a novel discrete gradient method for their computation.

## Key findings

- Established criteria for extrema existence on fractals
- Developed a discrete gradient algorithm for extremum search
- Demonstrated the algorithm's effectiveness on self-similar sets

## Abstract

We outline necessary and sufficient condition to the existence of extrmas of a function on a self-similar set, and we describe discrete gradient algorithm to find the extrema.