When optimizing functions which are computationally expensive and/or noisy, gradient information is often impractical to obtain or inaccurate. As a result, so-called ‘derivative-free’ optimization (DFO) methods are a suitable alternative. In this talk, I will show how existing methods for interpolation-based DFO can be extended to nonconvex problems with convex constraints, accessed only through projections. I will introduce a worst-case complexity analysis and show how existing geometric considerations of model accuracy (from the unconstrained setting) can be generalized to the constrained case. I will then show numerical results in the case of nonlinear least-squares optimization. This is joint work with Matthew Hough (University of Queensland and University of Waterloo).