Melodie Mouffe : May 31, 2006

Use of multi-level trust-region techniques for nonlinear bound constrained optimization problems.

Abstract

Trust-region methods are well-known optimization methods that are very efficient in solving nonlinear optimization problems. They are globally convergent in the sense that they converge from any starting point. Moreover they have quadratic convergence rate when close enough to the solution because they reduce then to Newton method (under suitable model choice). When solving an optimization problem resulting from the discretizatin of a continuous problem it is possible to use several discretization steps. Solving the problem with larger mesh size will give less accurate but cheaper solutions. These are used to provide good starting points for the finest level of discretization. The treatment of bound constrained problems by a multilevel trust-region algorithm introduces a new question: How to define the bounds on a coarser level ? In this talk we will draw an overview of multilevel trust-region methods and develop issues linked to the treatment of such bound constrained problems.