Numerical experience with a recursive trust-region method for multilevel nonlinear optimization

We consider an implementation of the recursive multilevel trust-region algorithm proposed by Gratton, Sartenaer and Toint (2004), and provide signicant numerical ex-perience on multilevel test problems. A suitable choice of the algorithm's parameters is identi ed on these problems, yielding a very satisfactory compromise between reliability and eciency. The resulting default algorithm is then compared to alternative optimiza-tion techniques such as mesh renement and direct solution of the ne-level problem. The sensibility of the default variant with respect to most important algorithmic parameters is nally investigated