We consider an implementation of the recursive multilevel trust-region algorithm proposed by Gratton et al. (A recursive trust-region method in infinity norm for bound-constrained nonlinear optimization, IMA J. Numer. Anal. 28(4) (2008), pp. 827-861) for bound-constrained nonlinear problems, and provide numerical experience on multilevel test problems. A suitable choice of the algorithm's parameters is identified on these problems, yielding a satisfactory compromise between reliability and efficiency. The resulting default algorithm is then compared with alternative optimization techniques such as mesh refinement and direct solution of the fine-level problem. It is also shown that its behaviour is similar to that of multigrid algorithms for linear systems.
Gratton, S., Mouffe, M., Sartenaer, A., Toint, P., & Tomanos, D. (2010). Numerical experience with a recursive trust-region method for multilevel nonlinear bound-constrained optimization. Optimization Methods and Software, 25(3), 359-386. https://doi.org/10.1080/10556780903239295