# Zeroth-Order Constrained Optimization from a Control Perspective via Feedback Linearization

arXiv: https://arxiv.org/abs/2509.24056 · HTML: https://mlsanity.com/paper/2509.24056/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2025.

## Built on by (most cited first, 1 of 1)

- [AdamFLIP: Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN Training](https://mlsanity.com/paper/2605.08408/) (2026)

## Abstract (arXiv)

Safe derivative-free optimization under unknown constraints is a fundamental challenge in modern learning and control. Existing zeroth-order (ZO) methods typically still assume access to a first-order oracle of the constraint functions or restrict attention to convex settings, leaving nonconvex optimization with black-box constraints largely unexplored. We propose the zeroth-order feedback-linearization (ZOFL) algorithm for ZO constrained optimization that enforces feasibility without access to the first-order oracle of the constraint functions and applies to both equality and inequality constraints. The proposed approach relies only on noisy, sample-based gradient estimates obtained via two-point estimators, yet provably guarantees constraint satisfaction under mild regularity conditions. It adopts a control-theoretic perspective on ZO constrained optimization and leverages feedback linearization, a nonlinear control technique, to enforce feasibility. Finite-time bounds on constraint violation and asymptotic global convergence guarantees are established for the ZOFL algorithm. A midpoint discretization variant is further developed to improve feasibility without sacrificing optimality. Empirical results demonstrate that ZOFL consistently outperforms standard ZO baselines, achieving competitive objective values while maintaining feasibility.