A recursive multi-level trust-region algorithm for bound constrained optimization
 
 
Description:  We consider the solution of large scale optimization problems, subject to bound constaints, arising in the discretization of infinite dimensional problems. In particular, we suppose that we have access to a collection of functions representing the problem for different value of a discretization parameter, ranging from the coarsest level, where computations are cheap, to the finest level. As in multigrid methods, our idea is to combine approximate solutions of the problems at all available levels, to obtain a fast algorithm for solving the problem at the finest level. Starting from an existing multi-level trust-region algorithm for unconstrained optimization, where the trust region is based on the Euclidean norm, we design an infinity norm variant, that is better suited to bound constrained problems and exploit the multi-level structure. The resulting solution method, that depends on some algorithmic parameters, is then shown to be convergent to first order critical point, from an arbitrarily chosen starting point. Using a set of test-cases arising from the calculus of variations, we determine reasonable values for the algorithmic parameters and compare the obtained algorithm with both a traditional trust-region technique, and with a mesh refinement strategy. We conclude with a discussion on stopping criteria for bound-constrained discretized problems that naturally take into account the discretization errors as does the backward error approach in linear algebra.
Area(s):
Date:  2008-12-11
Start Time:   11:30
Speaker:  Serge Gratton (CNES-CERFACS)
Place:  5.5
Research Groups: -Numerical Analysis and Optimization
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