A globally convergent primal-dual interior-point filter method for nonlinear programming: new filter optimality measures and computational results

• Main Author: Silva, Renata
• Publication Date: 2008
• Other Authors: Ulbrich, Michael, Ulbrich, Stefan, Vicente, Luís Nunes
• Format: Other
• Language: eng
• Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Download full: https://hdl.handle.net/10316/11218
• topic: Interior-point methods; Primal-dual; Filter; Global convergence; Largescale NLP

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.