Model-Based Derivative-Free Methods for Convex-Constrained Optimization

We present a model-based derivative-free method for optimization subject to general convex constraints, which we assume are unrelaxable and accessed only through projection operator that is cheap evaluate. prove global convergence worst-case complexity of $O(\epsilon^{-2})$ iterations objective evaluations nonconvex functions, matching results the unconstrained case. introduce new, weaker requirements on model accuracy compared existing methods. As result, sufficiently accurate interpolation models can be constructed using feasible points. develop comprehensive theory set management in this regime linear composite models. implement our approach nonlinear least-squares problems demonstrate strong practical performance general-purpose solvers.