Abstract
We consider an implementation of a recursive model-based active-set trust-region method for solving bound-constrained nonlinear non-convex optimization problems without derivatives using the technique of self-correcting geometry proposed in K. Scheinberg and Ph.L. Toint [Self-correcting geometry in model-based algorithms for derivative-free unconstrained optimization. SIAM Journal on Optimization, (to appear), 2010]. Considering an active-set method in bound-constrained model-based optimization creates the opportunity of saving a substantial amount of function evaluations. It allows US to maintain much smaller interpolation sets while proceeding optimization in lower-dimensional subspaces. The resulting algorithm is shown to be numerically competitive.
Acknowledgements
The second author gratefully acknowledges the partial support of the ADTAO project funded by the ‘Sciences et Technologies pour l'Aéronautique et l'Espace (STAE)’ Fundation (Toulouse, France) within the ‘Réseau Thématique de Recherche Avancée (RTRA)’.
Notes
Except for the case of ‘dummy points’, see Section 3.3.
BIGGS3, BOX2.
CHEBYQAD.
ENGVAL2, HATFLDD, HATFLDE.
EG1, EXPLIN, HART6, HS2, KOEBHELB, MAXLIKA, WEEDS.
Unfortunately, we could not conduct a detailed comparison of our results with the method proposed by these authors.