Global convergence of general derivative-free trust-region algorithms to first and second order critical points

摘要

In this paper we prove global convergence for first and second-order stationaritypoints of a class of derivative-free trust-region methods for unconstrainedoptimization. These methods are based on the sequential minimization of linear orquadratic models built from evaluating the objective function at sample sets. Thederivative-free models are required to satisfy Taylor-type bounds but, apart fromthat, the analysis is independent of the sampling techniques.A number of new issues are addressed, including global convergence when acceptanceof iterates is based on simple decrease of the objective function, trust-regionradius maintenance at the criticality step, and global convergence for second-ordercritical points.