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Title: Complexity and global rates of trust-region methods based on probabilistic models
Authors: Gratton, S
Royer, CW
Vicente, LN
Zhang, Z 
Keywords: Probabilistic models
Trust-region methods
Worst-case complexity
Issue Date: 2018
Publisher: Oxford University Press
Source: IMA journal of numerical analysis, 2018, v. 38, no. 3, p. 1579-1597 How to cite?
Journal: IMA journal of numerical analysis 
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- A nd 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.
ISSN: 0272-4979
EISSN: 1464-3642
DOI: 10.1093/imanum/drx043
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