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https://hdl.handle.net/10316/89439
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. | URI: | https://hdl.handle.net/10316/89439 | DOI: | 10.1093/imanum/drx043 | Rights: | openAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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