A matrix-free trust-region newton algorithm for convex-constrained optimization

We describe a matrix-free trust-region algorithm for solving convex-constrained optimization problems that uses the spectral projected gradient method to compute trial steps. To project onto the intersection of the feasible set and the trust region, we reformulate and solve the dual projection problem as a one-dimensional root finding problem. We demonstrate our algorithm's performance on various problems from data science and PDE-constrained optimization. Our algorithm shows superior performance when compared with five existing trust-region and spectral projected gradient methods, and has the added benefit that it is simple to implement.