An active-set trust-region method for derivative-free nonlinear bound-constrained optimization

Serge Gratton, Philippe Toint, Anke Tröltzsch

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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. © 2011 Taylor & Francis.
Original languageEnglish
Pages (from-to)873-894
Number of pages22
JournalOptimization Methods and Software
Issue number4-5
Publication statusPublished - 1 Aug 2011


  • trust region
  • active-set methods
  • bound constraints
  • numerical experiments
  • nonlinear optimization
  • derivative-free optimization


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