# Safe Zeroth-Order Convex Optimization Using Quadratic Local Approximations

arXiv: https://arxiv.org/abs/2211.02645 · HTML: https://mlsanity.com/paper/2211.02645/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2022.

## Built on by (most cited first, 2 of 2)

- [Principled Preferential Bayesian Optimization](https://mlsanity.com/paper/2402.05367/) (2024)
- [Safe Online Convex Optimization with Multi-Point Feedback](https://mlsanity.com/paper/2407.11471/) (2024)

## Abstract (arXiv)

We address black-box convex optimization problems, where the objective and constraint functions are not explicitly known but can be sampled within the feasible set. The challenge is thus to generate a sequence of feasible points converging towards an optimal solution. By leveraging the knowledge of the smoothness properties of the objective and constraint functions, we propose a novel zeroth-order method, SZO-QQ, that iteratively computes quadratic approximations of the constraint functions, constructs local feasible sets and optimizes over them. We prove convergence of the sequence of the objective values generated at each iteration to the minimum. Through experiments, we show that our method can achieve faster convergence compared with state-of-the-art zeroth-order approaches to convex optimization.