We consider an implementation of the recursive multilevel trust-region algorithm proposed by Gratton, Sartenaer, Toint (2004), and provide significant numerical experience on multilevel test problems. A suitable choice of the algorithm's parameters is identified on these problems, yielding a very satisfactory compromise between reliability and efficiency. The resulting default algorithm is then compared to alternative optimization techniques such as mesh refinement and direct solution of the fine-level problem. The sensibility of the default variant with respect to most important algorithmic parameters is finally investigated.
Technical Report 06/01, Department of Mathematics, University of Namur, Namur, Belgium, 2006.