We present new developments in the context of multilevel trust-region methods for nonlinear optimization. Motivated by the results obtained for unconstrained problems, we have extended the convergence theory for bound-constrained problems and for the use of infinity-norm trust regions. As an alternative for these methods, we have developed an algo- rithm that uses multilevel techniques for the exact resolution of the trust-region subproblem. This new method guarantees the convergence of the trust-region algorithm to a second-order critical point, with a much reduced associated cost when compared to classical methods. Un- fortunately, there are problems for which we cannot compute the derivatives of the objective function. The methods used today to solve this kind of problems are limited by the cost of the objective function computation. We present a multilevel version of one of these methods, that allows for the treatment of larger instances of the problem, as well as numerical results obtained with this new algorithm.
Multilevel optimization: convergence theory, algorithms and application to derivative-free optimization
Weber Mendonça, M. (Author). 3 Sept 2009
Student thesis: Doc types › Doctor of Sciences