A recursive trust-region method is introduced for the solution of bound-cons-trained nonlinear nonconvex optimization problems for which a hierarchy of descriptions exists. Typical cases are infinite-dimensional problems for which the levels of the hierarchy correspond to discretization levels, from coarse to fine. The new method uses the infinity norm to define the shape of the trust region, which is well adapted to the handling of bounds and also to the use of successive coordinate minimization as a smoothing technique. Numerical tests motivate a theoretical analysis showing convergence to first-order critical points irrespective of the starting point.
Gratton, S., Mouffe, M., Toint, P., & Weber-Mendona, M. (2008). A recursive ℓ-trust-region method for bound-constrained nonlinear optimization. IMA Journal of Numerical Analysis, 28(4), 827-861. https://doi.org/10.1093/imanum/drn034