Journal
SIAM JOURNAL ON OPTIMIZATION
Volume 20, Issue 1, Pages 387-415Publisher
SIAM PUBLICATIONS
DOI: 10.1137/060673424
Keywords
trust-region methods; derivative-free optimization; nonlinear optimization; global convergence
Categories
Funding
- FCT [POCI/59442/MAT/2004, PTDC/MAT/64838/2006]
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In this paper we prove global convergence for first- and second-order stationary points of a class of derivative-free trust-region methods for unconstrained optimization. These methods are based on the sequential minimization of quadratic (or linear) models built from evaluating the objective function at sample sets. The derivative-free models are required to satisfy Taylor-type bounds, but, apart from that, the analysis is independent of the sampling techniques. A number of new issues are addressed, including global convergence when acceptance of iterates is based on simple decrease of the objective function, trust-region radius maintenance at the criticality step, and global convergence for second-order critical points.
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