## Introduction

### Motivation and Set-up

A general optimisation question can be formulated by asking to minimise an objective function $f : \mathbb{R}^n \to \mathbb{R}$, which means finding: \begin{align*} x^* = \mathrm{argmin}_{x \in \mathbb{R}^n} f(x) \end{align*}

Depending on the nature of $f$, different settings may be considered:

• Convex vs non-convex objective functions;
• Differentiable vs non-differentiable objective functions;
• Allowed function or gradient computations;
• Noisy/Stochastic oracle access.

For the purpose of this paper, we consider convex smooth objective noiseless functions, where we have access to function computations but not gradient computations.