# Derivative-free optimization methods

## TL;DR

This paper reviews recent advances in derivative-free optimization methods, focusing on their categorization, applications, and developments for black-box functions in scientific, engineering, and AI problems.

## Contribution

It provides a comprehensive overview and unification of recent developments in derivative-free optimization, highlighting different problem settings and methodological approaches.

## Key findings

- Categorization of methods based on function properties
- Overview of deterministic and randomized approaches
- Discussion of methods for stochastic and constrained problems

## Abstract

In many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization. We provide a review and perspectives on developments in these methods, with an emphasis on highlighting recent developments and on unifying treatment of such problems in the non-linear optimization and machine learning literature. We categorize methods based on assumed properties of the black-box functions, as well as features of the methods. We first overview the primary setting of deterministic methods applied to unconstrained, non-convex optimization problems where the objective function is defined by a deterministic black-box oracle. We then discuss developments in randomized methods, methods that assume some additional structure about the objective (including convexity, separability and general non-smooth compositions), methods for problems where the output of the black-box oracle is stochastic, and methods for handling different types of constraints.