Derivative-Free Optimization Algorithms based on Non-Commutative Maps

TL;DR

This paper introduces a new class of derivative-free optimization algorithms that leverage non-commutative maps to approximate gradients, with proven convergence and demonstrated through simulations.

Contribution

It presents a novel approach using non-commutative maps for derivative-free optimization, expanding the toolkit for gradient approximation methods.

Findings

Algorithms converge under specified conditions.

Simulation results validate the effectiveness of the approach.

The method outperforms some existing derivative-free techniques.

Abstract

A novel class of derivative-free optimization algorithms is developed. The main idea is to utilize certain non-commutative maps in order to approximate the gradient of the objective function. Convergence properties of the novel algorithms are established and simulation examples are presented.