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

Authors:
Serge Gratton;Melodie Mouffe;Annick Sartenaer;Philippe L. Toint;Dimitri Tomanos
Affiliations:
CERFACS, av. G. Coriolis, Toulouse, France;CERFACS, av. G. Coriolis, Toulouse, France;Department of Mathematics, University of Namur, Namur, Belgium;Department of Mathematics, University of Namur, Namur, Belgium;Department of Mathematics, University of Namur, Namur, Belgium
Venue:
Optimization Methods & Software - The 2nd Veszprem Optimization Conference: Advanced Algorithms (VOCAL), 13-15 December 2006, Veszprem, Hungary
Year:
2010

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Abstract

We consider an implementation of the recursive multilevel trust-region algorithm proposed by Gratton et al. (A recursive trust-region method in infinity norm for bound-constrained nonlinear optimization, IMA J. Numer. Anal. 28(4) (2008), pp. 827-861) for bound-constrained nonlinear problems, and provide numerical experience on multilevel test problems. A suitable choice of the algorithm's parameters is identified on these problems, yielding a satisfactory compromise between reliability and efficiency. The resulting default algorithm is then compared with alternative optimization techniques such as mesh refinement and direct solution of the fine-level problem. It is also shown that its behaviour is similar to that of multigrid algorithms for linear systems.