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Global Convergence of General Derivative-Free Trust-Region Algorithms to First and Second Order Critical Points

A. R. Conn (arconn***at***us.ibm.com)
K. Scheinberg (katyas***at***us.ibm.com)
L. N. Vicente (lnv***at***mat.uc.pt)

Abstract: In this paper we prove global convergence for first and second-order stationarity points of a class of derivative-free trust-region methods for unconstrained optimization. These methods are based on the sequential minimization of linear or quadratic 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.

Keywords: trust-region methods, derivative-free optimization, nonlinear optimization, global convergence

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: Preprint 06-49, Department of Mathematics, University of Coimbra, Portugal, October 2006

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Entry Submitted: 10/26/2006
Entry Accepted: 10/26/2006
Entry Last Modified: 10/26/2006

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