DFBGN is a Python library for solving nonlinear least-squares problems. It is a derivative-free solver, meaning it only requires function values, and no first (or higher) derivatives. As a result, it is particularly useful for situations when function evaluations are expensive, or when they are noisy. Compared to DFO-LS, it is better-suited to large-scale problems (i.e. with many variables to be optimized).
This package is described in Chapter 7 of my doctoral thesis. A standalone paper is currently in preparation.