Complexity and global rates of trust-region methods based on probabilistic models

• Autor(a) principal: Gratton, Serge
• Data de Publicação: 2018
• Outros Autores: Royer, Clément W, Vicente, Luís Nunes, Zhang, Zaikun
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10316/89439; https://doi.org/10.1093/imanum/drx043
• topic: Trust-region methods; Worst-case complexity; Probabilistic models.

Trust-region algorithms have been proved to globally converge with probability 1 when the accuracy of the trust-region models is imposed with a certain probability conditioning on the iteration history. In this article, we study the complexity of such methods, providing global rates and worst-case complexity bounds on the number of iterations (with overwhelmingly high probability), for both first- and second-order measures of optimality. Such results are essentially the same as the ones known for trust-region methods based on deterministic models. The derivation of the global rates and worst-case complexity bounds follows closely from a study of direct search methods based on the companion notion of probabilistic descent.