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Global Convergence of General Derivative-Free Trust-Region Algorithms to First- and Second-Order Critical Points
Abstract
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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Cited by
Derivative-free optimization: a review of algorithms and comparison of software implementations
Rios, L. M., & Sahinidis, N. V. (2013) · Journal of Global Optimization · doi:10.1007/s10898-012-9951-y · Cited by 1,276
Benchmarking Derivative-Free Optimization Algorithms
Moré, J. J., & Wild, S. M. (2009) · SIAM Journal on Optimization · doi:10.1137/080724083 · Cited by 573
Metadata
- Authors
- Conn, A. R., Scheinberg, K., & Vicente, L. N.
- Venue
- SIAM Journal on Optimization
- Published
- 2009-01
- Volume
- 20
- Issue
- 1
- Pages
- 387-415
- ISSN
- 1052-6234 (ISSN-L)
- 1095-7189
- OpenAlex
- W2167511885
- Cited by
- 213
- References
- 0
- FWCI
- 13.09
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Global Convergence of General Derivative-Free Trust-Region Algorithms to First- and Second-Order Critical Points. https://app.cochat.ai/papers/10.1137/060673424
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- Conn, A. R., Scheinberg, K., & Vicente, L. N. (2009). Global Convergence of General Derivative-Free Trust-Region Algorithms to First- and Second-Order Critical Points. SIAM Journal on Optimization. https://doi.org/10.1137/060673424
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