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Title: Complexity and global rates of trust-region methods based on probabilistic models
Authors: Gratton, Serge
Royer, Clément W
Vicente, Luís Nunes
Zhang, Zaikun
Keywords: Trust-region methods; Worst-case complexity; Probabilistic models.
Issue Date: Jul-2018
Publisher: Oxford University Press - Institute of Mathematics and its Applications
Project: CMUC-UID/MAT/00324/2013 
Serial title, monograph or event: IMA Journal of Numerical Analysis
Volume: 38
Issue: 3
Abstract: 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.
DOI: 10.1093/imanum/drx043
Rights: openAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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