Global convergence of general derivative-free trust-region algorithms to first ...

• Author(s): Conn, Andrew R. ; Scheinberg, Katya ; Vicente, Luís Nunes
• Date: 2006
• Persistent ID: http://hdl.handle.net/10316/11325
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Trust-region methods; Derivative-free optimization; Nonlinear optimization; Global convergence
• Document Type: Preprint
• Language: English

Description

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. Centro de Matemática da Universidade de Coimbra; FCT under grant POCI/59442/MAT/2004